In this paper, the partitioned second derivative general linear methods for solving separable Hamiltonian problems are derived which are G-symplectic, interchange symmetry and have zero parasitic growth factors. Order conditions for such methods based on the theory of rooted trees are provided and examples of partitioned pairs of order 2 and 3 are given. The experiments have been performed on some

In this article, we have presented the controllability relationship between the semilinear control system of fractional order (1, 2] with delay and that of the semilinear control system without delay. Suppose X and U be Hilbert spaces which are separable and \(Z=L_2[0,b;X],\;Z_h=L_2[-h,b;X],\;0\le h\le b\) and \(Y=L_2[0,b;U]\) be the function spaces. Let the semilinear control system of fractional

In the present work, a generalized fractional integral operational matrix is derived by using classical Legendre wavelets. Then, a numerical scheme based on this operational matrix and Lagrange multipliers is proposed for solving variational problems with fractional order. This approach has been applied on some illustrative examples. The results obtained for these examples demonstrate that the suggested

Brooks’ theorem states that for a graph G, if \(\varDelta (G)\ge 3\), then \(\chi (G)\le \max \{\varDelta (G),\omega (G)\}\). Borodin and Kostochka conjectured a result strengthening Brooks’ theorem, stated as, if \(\varDelta (G)\ge 9\), then \(\chi (G)\le \max \{\varDelta (G)-1,\omega (G)\}\). This conjecture is still open for general graphs. In this paper, we show that the conjecture is true for

The main purpose of this paper is to construct a semi-implicit difference scheme for the multi-term time-fractional Burgers-type equations. Firstly, the L2-discretization formula is applied to the discretization of the multi-term Caputo fractional derivatives. Secondly, the second-order spatial derivative is approximated by using the second-order central difference quotient approximation and the nonlinear

In this paper, we present an improvement of the Hexagonal Shepard method which uses functional and first order derivative data. More in details, we use six-point basis functions in combination with the modified local interpolant on six-points. The resulting operator reproduces polynomials up to degree 3 and has quartic approximation order. Several numerical results show the good accuracy of approximation

In the existing definition of a neutrosophic planar graph, there is a limitation. In that definition, the value of falsity in degree of planarity is 1, even then the crisp underline graph is planar. This limitation is removed in the proposed definition. In this study, an advanced concept of the neutrosophic planar graphs is given and investigated the generalized neutrosophic planar graphs (GNPG). The

The all-at-once system arising from fractional mobile/immobile advection–diffusion equations is studied. Firstly, the finite difference method with L1 formula is employed to discretize it. The resulting implicit scheme is a time-stepping scheme, which is not suitable for parallel computing. Based on this scheme, an all-at-once system is established, which will be suitable for parallel computing. Secondly

In this paper, a fractional order eco-epidemiological model with nonlinear incidence rate is studied. The populations are divided into healthy prey, infected prey and predator. A prey refuge was introduced in the healthy prey population to make the model more realistic. Various qualitative properties including local and global stability analysis of equilibrium points are investigated. The theoretical

The primary target of present research is to examine the application of OHAM (optimal homotopy asymptotic method) for a nanofluid transport through Darcy Forchheimer space toward the stagnation region by comparing stretching and straining forces. The porous matrix is suspended with nanofluid, and the flow field is under inconsistent heat source/sink influence. The solutions of guiding boundary layer

In the Distributed Storage Systems (DSSs), the encoded fraction of information is stored in a distributed fashion on different chunk servers. Recently a new paradigm of Fractional Repetition (FR) codes has been introduced, in which, encoded data information is stored on distributed servers using an encoding involving a Maximum Distance Separable (MDS) code and a Repetition code. In this work, we have

A complex neutrosophic set is a useful model to properly handle incomplete information of periodic nature. This is characterized by three complex-valued components: truth, indeterminacy and falsity membership functions, whose range is extended from [0, 1] to unit circle in the complex plane. In this article, we define the notion of generalized complex neutrosophic graphs of type 1 and discuss certain

The purpose of the paper is to elucidate by global-dual contact holonomy why one might expect the Foucault spherical pendulum’s spin echo-stabilized, symplectic swing-plane through the rotation axis of the spinning earth to follow a parallel vector field as time passes at a velocity depending on the latitude of the swivel’s location. The spinor geometric foundations of the paradigmatic Foucault spherical

The aim of this paper is to investigate the existence, uniqueness and continuous dependence of solutions for a class of third order iterative differential equations with integral boundary conditions. The method applied here is based on Schauder’s fixed point theorem. The main idea consists to convert the considered equation into an integral one before using the fixed point theorem. Moreover, an example

By making use of the preconditioned Hermitian and skew-Hermitian splitting (PHSS) iteration as the inner solver for the modified Newton method, we establish the modified Newton-PHSS method for solving large sparse systems of nonlinear equations with positive definite Jacobian matrices at the solution points. Moreover, the local convergence theorem is proved under proper conditions. Numerical results

A boundary-value problem for singularly perturbed second order differential-difference equation with both the negative(delay) and positive(advance) shifts is considered and a new exponentially fitted three term finite difference scheme is proposed for the numerical approximation of its solution. An approximate version of the considered problem is constructed by the use of Taylor’s series expansion

In this paper, a general nonlinear Chikungunya virus (CHIKV) dynamics model is formulated and analyzed. We assume that, the production, removal and proliferation rates of all compartments as well as the incidence rate of infection are modeled by general nonlinear functions that satisfy a set of reasonable conditions. The model is incorporated by two types of discrete time delays. We prove the nonnegativity

We investigate the solution of linear systems of equations that arise when singularly perturbed reaction–diffusion partial differential equations are solved using a standard finite difference method on layer adapted grids. It is known that there are difficulties in solving such systems by direct methods when the perturbation parameter, \(\varepsilon \), is small (MacLachlan and Madden in SIAM J Sci

Cigarette smoking on college campuses has become a significant public health issue, which in turn led to an increasing focus on establishing programs to reduce its prevalence. In this paper, a compartmental model depicting the spread and cessation of the smoking habit on college campuses, obtained using theoretical principles often employed in mathematical epidemiology, is proposed and analysed. The

This paper considers the exact solution of Burgers’ hierarchy of nonlinear evolution equations. We construct the general nth conservation law of the hierarchy and prove that these expressions may be transformed into ordinary differential equations. In particular, a coordinate transformation leads to the systematic reduction of the conservation law properties of the Burgers’ hierarchy. Such an approach

This article proposes a mathematical model based on ordinary nonlinear differential equations that describes the dynamics of population growth of the mosquito Aedes aegypti throughout its life cycle. Then, a modification is made to the model by implementing a time delay, initially constant and then distributed over time. In addition, h, the population growth threshold, is established, the equilibrium

This work is considered in the framework of studies dedicated to the control problems, especially in epidemiology where the scientist are concerned to develop effective control strategies to minimize the number of infected individuals. In this paper, we set this problem as an asymptotic target control problem under mixed state-control constraints, for a general class of ordinary differential equations

In this paper, we propose an improved finite difference/finite element method for the fractional Rayleigh–Stokes problem with a nonlinear source term. The second-order backward differentiation formula (BDF2) and weighted and shifted Grünwald-Letnikov difference (WSGD) formula are employed to discretize first-order time derivative and the time fractional-order derivative, respectively. Moreover, a linearized

In this paper, we propose to investigate a new weighted statistical convergence by applying the Nörlund–Cesáro summability method. Based upon this definition, we prove some properties of statistically convergent sequences and a kind of the Korovkin type theorems. We also study the rate of the convergence for this kind of weighted statistical convergence and a Voronovskaya type theorem.

Mantle convection and melt migration are important processes for understanding Earth’s dynamics and how they relate to observations at the surface. Recently it has been established that melt migration can be modelled by coupling variable-viscosity Stokes flow and Darcy flow, where Stokes flow generally captures the long-term behaviour of the mantle and lithosphere, and Darcy flow models the two-phase

Globalization concepts for Newton-type iteration schemes are widely used when solving nonlinear problems numerically. Most of these schemes are based on a predictor/corrector step size methodology with the aim of steering an initial guess to a zero of f without switching between different attractors. In doing so, one is typically able to reduce the chaotic behavior of the classical Newton-type iteration

When seeking a solution to the interface problem, the potential theory to represent solution has been widely used. As the solution representation of the interface problem is only well-known for domains with simple inclusion, such as a disk, conformal mapping is often used to transform the arbitrary inclusion to a manageable inclusion to utilize the known solution representation. This paper proposes

Changes in morphology of a polycrystalline material may occur through interface motion under the action of a driving force. An important special case that is considered in this paper is the thermal grooving that occurs when a grain boundary intersects the flat surface of a recently solidified metal slab giving rise to the formation of a thin symmetric groove. In case the transient surface diffusion

Special number sequences play important role in many areas of science. One of them named as Fibonacci sequence dates back to 820 years ago. There is a lot of research on Fibonacci numbers due to their relation with the golden ratio and also due to many applications in Chemistry, Physics, Biology, Anthropology, Social Sciences, Architecture, Anatomy, Finance, etc. A slight variant of the Fibonacci sequence

The symmetric division deg index (or simply sdd-index) was proposed by Vukičević et al. as a remarkable predictor of total surface area of polychlorobiphenyls. It is one of discrete Adriatic indices that showed good predictive properties on the testing sets provided by International Academy of Mathematical Chemistry. In this paper, we investigate some properties of this graph invariant in terms of

Let V(G) and E(G) be, respectively, the vertex set and edge set of a graph G. The general sum-connectivity index of a graph G is denoted by \(\chi _\alpha (G)\) and is defined as \(\sum \limits _{uv\in E(G)}(d_u+d_v)^\alpha \), where uv is an edge that connect the vertices \(u,v\in V(G)\), \(d_u\) is the degree of a vertex u and \(\alpha \) is any non-zero real number. A cactus is a graph in which

In this paper, let p be a prime with \(p\ge 7\). We determine the weight distributions of cyclic codes of length 6 over \(\mathbb {F}_q\) and the minimum Hamming distances of all repeated-root cyclic codes of length \(6p^s\) over \(\mathbb {F}_q\), where q is a power of p and s is an integer. Furthermore, we find all maximum distance separable codes of length \(6p^s\).