Purpose

This paper aims to propose a novel approach based on uniform scale-3 Haar wavelets for unsteady state space fractional advection-dispersion partial differential equation which arises in complex network, fluid dynamics in porous media, biology, chemistry and biochemistry, electrode – electrolyte polarization, finance, system control, etc.

Design/methodology/approach

Scale-3 Haar wavelets are used to approximate the space and time variables. Scale-3 Haar wavelets converts the problems into linear system. After that Gauss elimination is used to find the wavelet coefficients.

Findings

A novel algorithm based on Haar wavelet for two-dimensional fractional partial differential equations is established. Error estimation has been derived by use of property of compactly supported orthonormality. The correctness and effectiveness of the theoretical arguments by numerical tests are confirmed.

Originality/value

Scale-3 Haar wavelets are used first time for these types of problems. Second, error analysis in new work in this direction.

中文翻译：

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基于3阶Haar小波的分数平流色散方程数值算法

目的

本文旨在提出一种基于均匀尺度 3 Haar 小波的新方法，用于在复杂网络、多孔介质中的流体动力学、生物学、化学和生物化学、电极 - 电解质极化、财务、系统控制等

设计/方法/方法

Scale-3 Haar 小波用于近似空间和时间变量。Scale-3 Haar 小波将问题转化为线性系统。然后用高斯消去法求小波系数。

发现

建立了一种基于Haar小波的二维分数式偏微分方程新算法。误差估计是通过使用紧支持正交性的性质推导出来的。通过数值试验验证了理论论证的正确性和有效性。

原创性/价值

Scale-3 Haar 小波首次用于这些类型的问题。二是新工作在这个方向上的误差分析。