Open Access

ARTICLE

A Novel Accurate Method for Multi-Term Time-Fractional Nonlinear Diffusion Equations in Arbitrary Domains

by Tao Hu¹, Cheng Huang², Sergiy Reutskiy^3,*, Jun Lu⁴, Ji Lin^5,*

1 Ningbo Yongxin Engineering Consulting Co., Ltd., Ningbo, 315042, China
2 Taizhou Huanfeng Water Conservancy Engineering Co., Ltd., Taizhou, 318050, China
3 A. Pidhornyi Institute of Mechanical Engineering Problems, National Academy of Sciences of Ukraine, Kharkiv, 61046, Ukraine
4 Material and Structure Department, Nanjing Hydraulic Research Institute, Nanjing, 210029, China
5 College of Mechanics and Materials, Hohai University, Nanjing, 211100, China

* Corresponding Authors: Sergiy Reutskiy. Email: ; Ji Lin. Email:

(This article belongs to the Special Issue: Advances on Mesh and Dimension Reduction Methods)

Computer Modeling in Engineering & Sciences 2024, 138(2), 1521-1548. https://doi.org/10.32604/cmes.2023.030449

Received 06 April 2023; Accepted 20 June 2023; Issue published 17 November 2023

Abstract

A novel accurate method is proposed to solve a broad variety of linear and nonlinear (1+1)-dimensional and (2+1)- dimensional multi-term time-fractional partial differential equations with spatial operators of anisotropic diffusivity. For (1+1)-dimensional problems, analytical solutions that satisfy the boundary requirements are derived. Such solutions are numerically calculated using the trigonometric basis approximation for (2+1)-dimensional problems. With the aid of these analytical or numerical approximations, the original problems can be converted into the fractional ordinary differential equations, and solutions to the fractional ordinary differential equations are approximated by modified radial basis functions with time-dependent coefficients. An efficient backward substitution strategy that was previously provided for a single fractional ordinary differential equation is then used to solve the corresponding systems. The straightforward quasilinearization technique is applied to handle nonlinear issues. Numerical experiments demonstrate the suggested algorithm’s superior accuracy and efficiency.

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Keywords

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