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A Numerical Study of Integrated Linear Reconstruction for Steady Euler Equations Based on Finite Volume Scheme Adv. Appl. Math. Mech. (IF 1.4) Pub Date : 20240101
Guanghui Hu,Ruo Li, Xucheng MengTowards the solution reconstruction, one of the main steps in Godunov type finite volume scheme, a class of integrated linear reconstruction (ILR) methods has been developed recently, from which the advantages such as parameters free and maximum principle preserving can be observed. It is noted that only timedependent problems are considered in the previous study on ILR, while the steady state problems

Numerical Computation of Helical Waves in a Finite Circular Cylinder Using Chebyshev Spectral Method Adv. Appl. Math. Mech. (IF 1.4) Pub Date : 20240101
XingLiang Lyu, WeiDong SuHelical waves are eigenfunctions of the curl operator and can be used to decompose an arbitrary threedimensional vector field orthogonally. In turbulence study, high accuracy for helical waves especially of high wavenumber is required. Due to the difficulty in analytical formulation, the more feasible strategy to obtain helical waves is numerical computation. For circular cylinders of finite length

Natural Frequencies of Composite Lattice Structure Surrounded by WinklerPasternak Ambient using Galerkin Method Adv. Appl. Math. Mech. (IF 1.4) Pub Date : 20240101
Ehsaneh Mohammadpour Hamedani, Amir H. HashemianThe present work contains an analytical expression and solution for free vibration problem of a composite lattice cylindrical shell surrounded by WinklerPasternak elastic foundation with clamped edges. The foundation is simulated using a large number of linear, homogenous shear and radial springs with variable stiffness. An integrated formula for calculation of the natural frequency of lattice structure

Effect of Thermal Convection and Mass Transfer on Particle Motion during Sedimentation: A Numerical Study Adv. Appl. Math. Mech. (IF 1.4) Pub Date : 20240101
Junjie Hu, Dongke SunThe sedimentation of a particle cluster with heat and mass transfer is studied with the lattice Boltzmann method. To investigate the effect of thermal convection and mass transfer on the motion of the particle cluster, four cases are studied, namely, without heat and mass transfer, with heat transfer, with mass transfer and with heat and mass transfer. Compared to mass transfer, the effect of thermal

A Fast Implementation of the Linear BondBased Peridynamic Beam Model Adv. Appl. Math. Mech. (IF 1.4) Pub Date : 20240101
Hao Tian,Xianchu Yang,Chenguang Liu, Guilin LiuWhile the theory of peridynamics (PD) holds significant potential in engineering, its application is often limited by the significant computational costs by the nonlocality of PD. This research is based on a threedimensional(3D) complex Timoshenko beam structure with six degrees of freedom. We propose a fast meshfree method based on the linear bondbased PD model of the stiffness matrix structure

Application of 2D GDQ Method to Analysis a Thick FG Rotating Disk with Arbitrarily Variable Thickness and NonUniform Boundary Conditions Adv. Appl. Math. Mech. (IF 1.4) Pub Date : 20240101
Hodais ZharfIn this paper twodimensional differential quadrature method has been used to analyze thick Functionally Graded (FG) rotating disks with nonuniform boundary conditions and variable thickness. Material properties vary continuously along both radial and axial directions by a power law pattern. Threedimensional solid mechanics theory is employed to formulate the axisymmetric problem as a second order

Implicit RungeKuttaNyström Methods with Lagrange Interpolation for Nonlinear SecondOrder IVPs with TimeVariable Delay Adv. Appl. Math. Mech. (IF 1.4) Pub Date : 20240101
Chengjian Zhang,Siyi Wang, Changyang TangThis paper deals with nonlinear secondorder initial value problems with timevariable delay. For solving this kind of problems, a class of implicit RungeKuttaNyström (IRKN) methods with Lagrange interpolation are suggested. Under the suitable condition, it is proved that an IRKN method is globally stable and has the computational accuracy $\mathcal{O}(h^{min\{p,\mu+ν+1\}}),$ where $p$ is the consistency

Calculation of FourDimensional Unsteady Gas Flow via Different Quadrature Schemes and RungeKutta 4th Order Method Adv. Appl. Math. Mech. (IF 1.4) Pub Date : 20240101
M. Salah,M. S. Matbuly,O. Civalek, Ola RagbIn this study, a (3+1) dimensional unstable gas flow system is applied and solved successfully via differential quadrature techniques based on various shape functions. The governing system of nonlinear fourdimensional unsteady Navier–Stokes equations of gas dynamics is reduced to the system of nonlinear ordinary differential equations using different quadrature techniques. Then, RungeKutta 4th order

New Finite Volume Mapped UnequalSized WENO Scheme for Hyperbolic Conservation Laws Adv. Appl. Math. Mech. (IF 1.4) Pub Date : 20240101
Yan Zhang, Jun ZhuThis article designs a new fifthorder finite volume mapped unequalsized weighted essentially nonoscillatory scheme (MUSWENO) for solving hyperbolic conservation laws on structured meshes. One advantage is that the new mapped WENOtype spatial reconstruction is a convex combination of a quartic polynomial with two linear polynomials defined on unequalsized central or biased spatial stencils. Then

Nonconforming Finite Element Methods for TwoDimensional Linearly Elastic Shallow Shell Model Adv. Appl. Math. Mech. (IF 1.4) Pub Date : 20240101
Rongfang Wu,Xiaoqin Shen,Dongyang Shi, Jiaping YuA shell whose height is far less than the minimum size covering the bottom is called the shallow shell. As a branch of linear elastic shell, it is a special shell with large span and has been widely applied in engineering fields. The main aim of this paper is to construct a general nonconforming finite element framework for a twodimensional shallow shell model proposed by Ciarlet and Miara. Based

Investigating Droplet and Bubble Deformation under Shear Flow Using the MultiPseudoPotential Scheme of Lattice Boltzmann Method Adv. Appl. Math. Mech. (IF 1.4) Pub Date : 20240101
Raheleh Sharif,Mostafa Varmazyar, Arash MohammadiIn the present study, a multipseudopotential model is used to simulate the deformation and breakup of bubbles and droplets under simple shear flow. It is shown that the current model can adjust the amount of surface tension, independent of the interface thickness, equation of state (EOS), and reduced temperature. Considering the available findings, no comprehensive study has been performed on all

An Analytical Approach for Buckling of FG Cylindrical Nanopanels Resting on Pasternak’s Foundations in the Thermal Environment Adv. Appl. Math. Mech. (IF 1.4) Pub Date : 20240101
Do Quang Chan,Bui Gia Phi,Nguyen Thi Thu Nga,MinhQuy Le, VanHieu DangIn this article, the effects of temperature and sizedependent on the buckling behavior of functionally graded (FG) cylindrical nanopanels resting on elastic foundation using nonlocal strain gradient theory are investigated in detail analytical approach. According to a simple powerlaw distribution, the material properties of FG cylindrical nanopanels are assumed to vary continuously through the thickness

Analysis of Weakly Nonlinear Evolution Characteristics of Flow in the Constant Curvature Bend Adv. Appl. Math. Mech. (IF 1.4) Pub Date : 20231201
Bin Li,Haijue Xu,Yuchuan Bai, Ziqing JiThe meandering river is an unstable system with the characteristic of nonlinearity, which results from the instability of the flow and boundary. Focusing on the hydrodynamic nonlinearity of the bend, we use the weakly nonlinear theory and perturbation method to construct the nonlinear evolution equations of the disturbance amplitude and disturbance phase of twodimensional flow in meandering bend.

A Hessian Recovery Based Linear Finite Element Method for Molecular Beam Epitaxy Growth Model with Slope Selection Adv. Appl. Math. Mech. (IF 1.4) Pub Date : 20231201
Minqiang Xu, Qingsong ZouIn this paper, we present a Hessian recovery based linear finite element method to simulate the molecular beam epitaxy growth model with slope selection. For the time discretization, we apply a firstorder convex splitting method and secondorder CrankNicolson scheme. For the space discretization, we utilize the Hessian recovery operator to approximate secondorder derivatives of a $C^0$ linear finite

A NitscheBased ElementFree Galerkin Method for Semilinear Elliptic Problems Adv. Appl. Math. Mech. (IF 1.4) Pub Date : 20231201
Tao Zhang, Xiaolin LiA Nitschebased elementfree Galerkin (EFG) method for solving semilinear elliptic problems is developed and analyzed in this paper. The existence and uniqueness of the weak solution for semilinear elliptic problems are proved based on a condition that the nonlinear term is an increasing Lipschitz continuous function of the unknown function. A simple iterative scheme is used to deal with the nonlinear

A HighOrder Localized Artificial Diffusivity Scheme for Discontinuity Capturing on 1D DriftFlux Models for GasLiquid Flows Adv. Appl. Math. Mech. (IF 1.4) Pub Date : 20231201
Adyllyson H. Nascimento, Eugênio S. RosaA computational code is developed for the numerical solution of onedimensional transient gasliquid flows using driftflux models, in isothermal and also with phase change situations. For these twophase models, classical upwind schemes such as Roe and Godunovtype schemes are generally difficult to derive and expensive to use, since there are no treatable analytic expressions for the Jacobian matrix

DPK: Deep Neural Network Approximation of the First PiolaKirchhoff Stress Adv. Appl. Math. Mech. (IF 1.4) Pub Date : 20231201
Tianyi Hu,Jerry Zhijian Yang, Cheng YuanThis paper presents a specific network architecture for approximation of the first PiolaKirchhoff stress. The neural network enables us to construct the constitutive relation based on both macroscopic observations and atomistic simulation data. In contrast to traditional deep learning models, this architecture is intrinsic symmetric, guarantees the frameindifference and materialsymmetry of stress

On the Characteristic Length Scale for the Synthetic Turbulence Based on the SpalartAllmaras Model Adv. Appl. Math. Mech. (IF 1.4) Pub Date : 20231201
Qilong Guo,Pengxin Liu,Chen Li,Dong Sun, Xianxu YuanIn the hybrid RANSLES simulations, proper turbulent fluctuations should be added at the RANStoLES interface to drive the numerical solution restoring to a physically resolved turbulence as rapidly as possible. Such turbulence generation methods mostly need to know the distribution of the characteristic length scale of the background RANS model, which is important for the recovery process. The approximation

A Compact Difference Scheme for TimeSpace Fractional Nonlinear DiffusionWave Equations with Initial Singularity Adv. Appl. Math. Mech. (IF 1.4) Pub Date : 20231201
Emadidin Gahalla Mohmed Elmahdi,Sadia Arshad, Jianfei HuangIn this paper, we present a linearized compact difference scheme for onedimensional timespace fractional nonlinear diffusionwave equations with initial boundary value conditions. The initial singularity of the solution is considered, which often generates a singular source and increases the difficulty of numerically solving the equation. The CrankNicolson technique, combined with the midpoint formula

A MassPreserving Characteristic Finite Difference Method For Miscible Displacement Problem Adv. Appl. Math. Mech. (IF 1.4) Pub Date : 20231201
Jiansong Zhang,Yue Yu,Rong Qin, Zhaohui LiuIn this article, a new characteristic finite difference method is developed for solving miscible displacement problem in porous media. The new method combines the characteristic technique with masspreserving interpolation, not only keeps mass balance but also is of secondorder accuracy both in time and space. Numerical results are presented to confirm the convergence and the accuracy in time and

A VertexCentered Arbitrary LagrangianEulerian Finite Volume Method with SubCells for TwoDimensional Compressible Flow Adv. Appl. Math. Mech. (IF 1.4) Pub Date : 20231201
Xiaolong Zhao,Xijun Yu,Zupeng Jia,Shijun Zou, Meilan QiuIn this paper, we present a new vertexcentered arbitrary LagrangianEulerian (ALE) finite volume scheme for twodimensional compressible flow. In our scheme, the momentum equation is discretized on the vertex control volume, while the mass equation and the energy equation are discretized on the subcells which are included in the vertex control volume. We attain the average of the fluid velocity on

Local Discontinuous Galerkin Methods with Decoupled ImplicitExplicit Time Marching for the GrowthMediated Autochemotactic Pattern Formation Model Adv. Appl. Math. Mech. (IF 1.4) Pub Date : 20231201
Hui Wang,Hui Guo,Jiansong Zhang, Lulu TianIn this paper, two fullydiscrete local discontinuous Galerkin (LDG) methods are applied to the growthmediated autochemotactic pattern formation model in selfpropelling bacteria. The numerical methods are linear and decoupled, which greatly improve the computational efficiency. In order to resolve the time level mismatch of the discretization process, a special time marching method with highorder

Reconstructing the Absorption Function in a QuasiLinear Sorption Dynamic Model via an Iterative Regularizing Algorithm Adv. Appl. Math. Mech. (IF 1.4) Pub Date : 20231201
Alexey Shcheglov,Jingzhi Li,Chao Wang,Alexander Ilin, Ye ZhangThis study addresses the parameter identification problem in a system of timedependent quasilinear partial differential equations (PDEs). Using the integral equation method, we prove the uniqueness of the inverse problem in nonlinear PDEs. Moreover, using the method of successive approximations, we develop a novel iterative algorithm to estimate sorption isotherms. The stability results of the algorithm

Free Vibration of Stiffened Plate with Cracked Stiffeners Adv. Appl. Math. Mech. (IF 1.4) Pub Date : 20231201
Jian Xue,Lihua Chen,Yue Sun, Wei ZhangIn this paper, a new cracked stiffener model for the stiffener with a partthrough and open crack is proposed, considering the compatibility condition of displacements between the plate and the stiffener. Based on the firstorder shear deformation theory, the free vibration of stiffened isotropic plates with cracked stiffeners are investigated for the first time. The description of the crack parameters

Edge Detectors Based on Pauta Criterion with Application to Hybrid CompactWENO Finite Difference Scheme Adv. Appl. Math. Mech. (IF 1.4) Pub Date : 20231001
Chunhua Zhang,Zhen Gao,Sa Ye, Peng LiIn the last two decades, many edge detection methods have been developed and widely used in image processing for edge detection and the hybrid compactWENO finite difference (hybrid) schemes for solving the system of hyperbolic conservation laws with solutions containing both discontinuous and complex finescale structures. However, many edge detection methods include the problemdependent parameters

Construction of NonEquilibrium Gas Distribution Functions Through Expansions in Peculiar Velocity Space Adv. Appl. Math. Mech. (IF 1.4) Pub Date : 20231001
Z. Y. Yuan,Z. Chen,C. Shu,Y. Y. Liu, Z. L. ZhangGas distribution function plays a crucial role in the description of gas flows at the mesoscopic scale. In the presence of nonequilibrium flow, the distribution function loses its rotational symmetricity, making the mathematical derivation difficult. From both the ChapmanEnskog expansion and the Hermite polynomial expansion (Grad’s method), we observe that the nonequilibrium effect is closely related

High Order Deep Domain Decomposition Method for Solving High Frequency Interface Problems Adv. Appl. Math. Mech. (IF 1.4) Pub Date : 20231001
Zhipeng Chang,Ke Li,Xiufen Zou, Xueshuang XiangThis paper proposes a high order deep domain decomposition method (HOrderDeepDDM) for solving highfrequency interface problems, which combines high order deep neural network (HOrderDNN) with domain decomposition method (DDM). The main idea of HOrderDeepDDM is to divide the computational domain into some subdomains by DDM, and apply HOrderDNNs to solve the highfrequency problem on each subdomain

A Quadratic Finite Volume Method for Parabolic Problems Adv. Appl. Math. Mech. (IF 1.4) Pub Date : 20231001
Yuanyuan Zhang, Xiaoping LiuIn this paper, a quadratic finite volume method (FVM) for parabolic problems is studied. We first discretize the spatial variables using a quadratic FVM to obtain a semidiscrete scheme. We then employ the backward Euler method and the CrankNicolson method respectively to further disctetize the time vatiable so as to derive two fulldiscrete schemes. The existence and uniqueness of the semidiscrete

Partial Topology Identification of Stochastic MultiWeighted Complex Networks Based on GraphTheoretic Method and Adaptive Synchronization Adv. Appl. Math. Mech. (IF 1.4) Pub Date : 20231001
Huiling Chen,Chunmei Zhang,Yuli Feng, Qin XuThis article aims to identify the partial topological structures of delayed complex network. Based on the driveresponse concept, a more universal model, which includes nonlinear couplings, stochastic perturbations and multiweights, is considered into driveresponse networks. Different from previous methods, we obtain identification criteria by combining graphtheoretic method and adaptive synchronization

A Coiflet Wavelet Homotopy Technique for Nonlinear PDEs: Application to the Extreme Bending of Orthotropic Plate with Forced Boundary Constraints Adv. Appl. Math. Mech. (IF 1.4) Pub Date : 20231001
Qiang Yu,Shuaimin Wang,Junfeng Xiao, Hang XuA generalized homotopybased Coiflettype wavelet method for solving strongly nonlinear PDEs with nonhomogeneous edges is proposed. Based on the improvement of boundary difference order by Taylor expansion, the accuracy in wavelet approximation is largely improved and the accumulated error on boundary is successfully suppressed in application. A unified highprecision wavelet approximation scheme is

A New WellBalanced Finite Volume CWENO Scheme for Shallow Water Equations over Bottom Topography Adv. Appl. Math. Mech. (IF 1.4) Pub Date : 20231001
Wei Guo,Ziming Chen,Shouguo Qian,Gang Li, Qiang NiuIn this article, we develop a new wellbalanced finite volume central weighted essentially nonoscillatory (CWENO) scheme for one and twodimensional shallow water equations over uneven bottom. The wellbalanced property is of paramount importance in practical applications, where many studied phenomena can be regarded as small perturbations to the steady state. To achieve the wellbalanced property

A Convex Approximation for a PDE Constrained Fractional Optimization Problem with an Application to Photonic Crystal Design Adv. Appl. Math. Mech. (IF 1.4) Pub Date : 20231001
Mengyue Wu,Jianhua Yuan, Jianxin ZhangBased on a subspace method and a linear approximation method, a convex algorithm is designed to solve a kind of nonconvex PDE constrained fractional optimization problem in this paper. This PDE constrained problem is an infinitedimensional Hermitian eigenvalue optimization problem with nonconvex and low regularity. Usually, such a continuous optimization problem can be transformed into a largescale

A NodeBased Smoothed Finite Element Method with Linear Gradient Fields for Elastic Obstacle Scattering Problems Adv. Appl. Math. Mech. (IF 1.4) Pub Date : 20231001
Junhong Yue,Yu Wang,Yan Li, Ming LiIn this paper, a nodebased smoothed finite element method (NSFEM) with linear gradient fields (NSFEML) is presented to solve elastic wave scattering by a rigid obstacle. By using Helmholtz decomposition, the problem is transformed into a boundary value problem with coupled boundary conditions. In numerical analysis, the perfectly matched layer (PML) and transparent boundary condition (TBC) are

Spectral Galerkin Approximation of Fractional Optimal Control Problems with Fractional Laplacian Adv. Appl. Math. Mech. (IF 1.4) Pub Date : 20231001
Jiaqi Zhang,Yin Yang, Zhaojie ZhouIn this paper spectral Galerkin approximation of optimal control problem governed by fractional elliptic equation is investigated. To deal with the nonlocality of fractional Laplacian operator the CaffarelliSilvestre extension is utilized. The first order optimality condition of the extended optimal control problem is derived. A spectral Galerkin discrete scheme for the extended problem based on weighted

Vibration Behavior of a Sandwich Porous Elliptical MicroShell with a MagnetoRheological Core Based on the Modified Couple Stress Theory Adv. Appl. Math. Mech. (IF 1.4) Pub Date : 20231001
A. Mohammadpour,S. Jafari Mehrabadi, P. YousefRecently, the use of porous materials has grown widely in many structures, such as beams, plates, and shells. The characteristics of porous materials change in the thickness direction by different functions. This study has investigated the free vibration analysis of a sandwich porous elliptical microshell with a magnetorheological fluid (MRF) core for the first time. Initially, we examined the displacement

A WellBalanced FVC Scheme for 2D Shallow Water Flows on Unstructured Triangular Meshes Adv. Appl. Math. Mech. (IF 1.4) Pub Date : 20230601
Moussa Ziggaf,Imad Kissami,Mohamed Boubekeur, Fayssal BenkhaldounThis paper aims to present a new wellbalanced, accurate and fast finite volume scheme on unstructured grids to solve hyperbolic conservation laws. It is a scheme that combines both finite volume approach and characteristic method. In this study, we consider a shallow water system with Coriolis effect and bottom friction stresses where this new Finite Volume Characteristics (FVC) scheme has been applied

A Reconstructed Discontinuous Approximation to MongeAmpère Equation in Least Square Formulation Adv. Appl. Math. Mech. (IF 1.4) Pub Date : 20230601
Ruo Li, Fanyi YangWe propose a numerical method to solve the MongeAmpère equation which admits a classical convex solution. The MongeAmpere equation is reformulated into an equivalent firstorder system. We adopt a novel reconstructed discontinuous approximation space which consists of piecewise irrotational polynomials. This space allows us to solve the firstorder system in two sequential steps. In the first step

A Finite Element Variational Multiscale Method for Stationary Incompressible Magnetohydrodynamics Equations Adv. Appl. Math. Mech. (IF 1.4) Pub Date : 20230601
Huayi Huang,Yunqing Huang, Qili TangIn this paper, we propose a variational multiscale method (VMM) for the stationary incompressible magnetohydrodynamics equations. This method is defined by largescale spaces for the velocity field and the magnetic field, which aims to solve flows at high Reynolds numbers. We provide a new VMM formulation and prove its stability and convergence. Finally, some numerical experiments are presented to

Numerical Simulations of the Richtmyer–Meshkov Instability of SolidVacuum Interface Adv. Appl. Math. Mech. (IF 1.4) Pub Date : 20230601
Xiangyi Liu,Zhiye Zhao,Nansheng Liu, Xiyun LuThe Richtmyer–Meshkov instability of interfaces separating elasticplastic materials from vacuum is investigated by numerical simulation using a multimaterial solid mechanics algorithm based on an Eulerian framework. The research efforts are directed to reveal the influence of the initial perturbation and material strength on the deformation of the perturbed interface impacted by an initial shock

A SelfAdaptive Algorithm of the Clean Numerical Simulation (CNS) for Chaos Adv. Appl. Math. Mech. (IF 1.4) Pub Date : 20230601
Shijie Qin, Shijun LiaoThe background numerical noise $ε_0$ is determined by the maximum of truncation error and roundoff error. For a chaotic system, the numerical error $ε(t)$ grows exponentially, say, $ε(t) = ε_0 {\rm exp}(κt),$ where $κ > 0$ is the socalled noisegrowing exponent. This is the reason why one can not gain a convergent simulation of chaotic systems in a long enough interval of time by means of traditional

Influence of the Radial Inertia Effect on the Propagation Law of Stress Waves in ThinWalled Tubes Adv. Appl. Math. Mech. (IF 1.4) Pub Date : 20230601
Shitang Cui, Yongliang ZhangThis investigation focused on the influence of the radial inertia effect on the propagation behavior of stress waves in thinwalled tubes subjected to combined longitudinal and torsional impact loads. Generalized characteristics theory was used to analyze the main features of the characteristic wave speeds and simple wave solutions in thinwalled tubes. The incremental elasticplastic constitutive

Arbitrarily HighOrder EnergyPreserving Schemes for the CamassaHolm Equation Based on the Quadratic Auxiliary Variable Approach Adv. Appl. Math. Mech. (IF 1.4) Pub Date : 20230601
Yuezheng Gong,Qi Hong,Chunwu Wang, Yushun WangIn this paper, we present a quadratic auxiliary variable (QAV) technique to develop a novel class of arbitrarily highorder energypreserving algorithms for the CamassaHolm equation. The QAV approach is first utilized to transform the original equation into a reformulated QAV system with a consistent initial condition. Then the reformulated QAV system is discretized by applying the Fourier pseudospectral

A ScaleInvariant Fifth Order WCNS Scheme for Hyperbolic Conservation Laws Adv. Appl. Math. Mech. (IF 1.4) Pub Date : 20230601
Zixuan Zhang,Yidao Dong,Huaibao Zhang,Shichao Zheng, Xiaogang DengIn this article, a robust, effective, and scaleinvariant weighted compact nonlinear scheme (WCNS) is proposed by introducing descaling techniques to the nonlinear weights of the WCNSZ/D schemes. The new scheme achieves an essentially nonoscillatory approximation of a discontinuous function (ENOproperty), a scaleinvariant property with an arbitrary scale of a function (Siproperty), and an optimal

On the Convergence of a CrankNicolson Fitted Finite Volume Method for Pricing European Options Under RegimeSwitching Kou’s JumpDiffusion Models Adv. Appl. Math. Mech. (IF 1.4) Pub Date : 20230601
Xiaoting Gan,Junfeng Yin, Rui LiIn this paper, we construct and analyze a CrankNicolson fitted finite volume scheme for pricing European options under regimeswitching Kou's jumpdiffusion model which is governed by a system of partial integrodifferential equations (PIDEs). We show that this scheme is consistent, stable and monotone as the mesh sizes in space and time approach zero, hence it ensures the convergence to the solution

Impacts of DownUp Hill Segment on the Threshold of Shock Formation of Ring Road Vehicular Flow Adv. Appl. Math. Mech. (IF 1.4) Pub Date : 20230601
Zejing Hu,M. N. Smirnova,N. N. Smirnov,Yongliang Zhang, Zuojin ZhuThe study of impacts of downup hill road segment on the density threshold of traffic shock formation in ring road vehicular flow is helpful to the deep understanding of sags’ bottleneck effect. Sags are freeway segments along which the gradient increases gradually in the traffic direction. The main aim of this paper is to seek the density threshold of shock formation of vehicular flow in ring road

A NonSingular Boundary Element Method for Interactions between Acoustical Field Sources and Structures Adv. Appl. Math. Mech. (IF 1.4) Pub Date : 20230401
Qiang SunLocalized point sources (monopoles) in an acoustical domain are implemented to a three dimensional nonsingular Helmholtz boundary element method in the frequency domain. It allows for the straightforward use of higher order surface elements on the boundaries of the problem. It will been shown that the effect of the monopole sources ends up on the right hand side of the resulting matrix system. Some

The Convergence of EulerMaruyama Method of Nonlinear VariableOrder Fractional Stochastic Differential Equations Adv. Appl. Math. Mech. (IF 1.4) Pub Date : 20230401
Shanshan Xu,Lin Wang, Wenqiang WangIn this paper, we first prove the existence and uniqueness theorem of the solution of nonlinear variableorder fractional stochastic differential equations (VFSDEs). We futher constructe the EulerMaruyama method to solve the equations and prove the convergence in mean and the strong convergence of the method. In particular, when the fractional order is no longer varying, the conclusions obtained are

Electroelastic Analysis of TwoDimensional Piezoelectric Structures by the Localized Method of Fundamental Solutions Adv. Appl. Math. Mech. (IF 1.4) Pub Date : 20230401
Yan Gu,Ji Lin, ChiaMing FanAccurate and efficient analysis of the coupled electroelastic behavior of piezoelectric structures is a challenging task in the community of computational mechanics. During the past few decades, the method of fundamental solutions (MFS) has emerged as a popular and wellestablished meshless boundary collocation method for the numerical solution of many engineering applications. The classical MFS formulation

A Coercivity Result of Quadratic Finite Volume Element Schemes over Triangular Meshes Adv. Appl. Math. Mech. (IF 1.4) Pub Date : 20230401
Xueying Wen, Yanhui ZhouIn this work, we study the coercivity of a family of quadratic finite volume element (FVE) schemes over triangular meshes for solving elliptic boundary value problems. The analysis is based on the standard mapping from the trial function space to the test function space so that the coercivity result can be naturally incorporated with most existing theoretical results such as $H^1$ and $L^2$ error estimates

A Partial RKDG Method for Solving the 2D Ideal MHD Equations Written in SemiLagrangian Formulation on Moving Meshes with Exactly DivergenceFree Magnetic Field Adv. Appl. Math. Mech. (IF 1.4) Pub Date : 20230401
Shijun Zou,Xijun Yu,Zihuan Dai,Fang Qing, Xiaolong ZhaoA partial RungeKutta Discontinuous Galerkin (RKDG) method which preserves the exactly divergencefree property of the magnetic field is proposed in this paper to solve the twodimensional ideal compressible magnetohydrodynamics (MHD) equations written in semiLagrangian formulation on moving quadrilateral meshes. In this method, the fluid part of the ideal MHD equations along with $z$component of

A Novel WaveletHomotopy Galerkin Method for Unsteady Nonlinear Wave Equations Adv. Appl. Math. Mech. (IF 1.4) Pub Date : 20230401
Yue Zhou, Hang XuThe Coiflet wavelethomotopy Galerkin method is extended to solve unsteady nonlinear wave equations for the first time. The Kortewegde Vries (KdV) equation, the Burgers equation and the Kortewegde VriesBurgers (KdVB) equation are examined as illustrative examples. Validity and accuracy of the proposed method are assessed in terms of relative variance and the maximum error norm. Our results are found

Broad Learning System with Preprocessing to Recover the Scattering Obstacles with Far–Field Data Adv. Appl. Math. Mech. (IF 1.4) Pub Date : 20230401
Weishi Yin,Hongyu Qi, Pinchao MengBased on Broad Learning System with preprocessing, the impenetrable obstacles were reconstructed. Firstly, the farfield data were preprocessed by Random Forest, and the shapes of the obstacles were classified by dividing the farfield data into different categories. Secondly, the broad learning system was employed for reconstructing the unknown scatterer. The farfield data of the scatterer were regarded

Numerical Investigation of the Pulsatile Flow of Viscous Fluid in Constricted Wall Channel with Thermal Radiation Adv. Appl. Math. Mech. (IF 1.4) Pub Date : 20230401
Amjad Ali,Zainab Bukhari,Hamayun Farooq, Zaheer AbbasThe main theme of the current article is to investigate the heat transfer in the pulsatile flow of an electrically conducting viscous fluid in a constricted channel under the effect of the magnetic field and thermal radiation. The unsteady governing equations simplified for low conducting fluids are solved numerically by finite difference method using streamvorticity function formulation. The influence

The Formulation of Finite Difference RBFWENO Schemes for Hyperbolic Conservation Laws: An Alternative Technique Adv. Appl. Math. Mech. (IF 1.4) Pub Date : 20230401
Rooholah Abedian, Mehdi DehghanTo solve conservation laws, efficient schemes such as essentially nonoscillatory (ENO) and weighted ENO (WENO) have been introduced to control the Gibbs oscillations. Based on radial basis functions (RBFs) with the classical WENOJS weights, a new type of WENO schemes has been proposed to solve conservation laws [J. Guo et al., J. Sci. Comput., 70 (2017), pp. 551–575]. The purpose of this paper is

Critical Transition Reynolds Number for the Incompressible Flatplate Boundary Layer as Searched by Numerical Simulation Adv. Appl. Math. Mech. (IF 1.4) Pub Date : 20230401
Yongming Zhang,Di Liu, Ning LiThe critical transition Reynolds number is the lowest value at which the turbulent flow can hold in real flows. The determination of the critical transition Reynolds number not only is a scientific problem, but also is important for some engineering problems. However, there is no available theoretical method to search the critical value. For the hypersonic boundary layer with significant importance

A MaximumPrinciplePreserving Finite Volume Scheme for Diffusion Problems on Distorted Meshes Adv. Appl. Math. Mech. (IF 1.4) Pub Date : 20230401
Dan Wu,Junliang Lv,Lei Lin, Zhiqiang ShengIn this paper, we propose an approach for constructing conservative and maximumprinciplepreserving finite volume schemes by using the method of undetermined coefficients, which depend nonlinearly on the linear nonconservative onesided fluxes. In order to facilitate the derivation of expressions of these undetermined coefficients, we explicitly provide a simple constriction condition with a scaling

Optimal Error Estimates of the SemiDiscrete Local Discontinuous Galerkin Method and Exponential Time Differencing Schemes for the Thin Film Epitaxy Problem Without Slope Selection Adv. Appl. Math. Mech. (IF 1.4) Pub Date : 20230201
Danni Zhang, Ruihan GuoIn this paper, we prove the optimal error estimates in $L^2$ norm of the semidiscrete local discontinuous Galerkin (LDG) method for the thin film epitaxy problem without slope selection. To relax the severe time step restriction of explicit time marching methods, we employ a class of exponential time differencing (ETD) schemes for time integration, which is based on a linear convex splitting principle

A Priori Error Estimates for Spectral Galerkin Approximations of Integral StateConstrained Fractional Optimal Control Problems Adv. Appl. Math. Mech. (IF 1.4) Pub Date : 20230201
Juan Zhang,Jiabin Song, Huanzhen ChenThe fractional optimal control problem leads to significantly increased computational complexity compared to the corresponding classical integerorder optimal control problem, due to the global properties of fractional differential operators. In this paper, we focus on an optimal control problem governed by fractional differential equations with an integral constraint on the state variable. By the

A Conservative SAVRRK Finite Element Method for the Nonlinear Schrödinger Equation Adv. Appl. Math. Mech. (IF 1.4) Pub Date : 20230201
Jun Yang, Nianyu YiIn this paper, we propose, analyze and numerically validate a conservative finite element method for the nonlinear Schrödinger equation. A scalar auxiliary variable (SAV) is introduced to reformulate the nonlinear Schrödinger equation into an equivalent system and to transform the energy into a quadratic form. We use the standard continuous finite element method for the spatial discretization, and

Unconditional Superconvergence Analysis of Energy Conserving Finite Element Methods for the Nonlinear Coupled KleinGordon Equations Adv. Appl. Math. Mech. (IF 1.4) Pub Date : 20230201
Ming Cui,Yanfei Li, Changhui YaoIn this paper, we consider the energy conserving numerical scheme for coupled nonlinear KleinGordon equations. We propose energy conserving finite element method and get the unconditional superconvergence result $\mathcal{O}(h^2+∆t^2 )$ by using the error splitting technique and postprocessing interpolation. Numerical experiments are carried out to support our theoretical results.