Analysis and numerical simulation for a class of time fractional diffusion equation via tension spline

被引：10

作者：

Kanth, A. S. V. Ravi ^{[1
]}

Sirswal, Deepika ^{[1
]}

机构：

[1] Natl Inst Technol, Dept Math, Kurukshetra 136119, Haryana, India

来源：

NUMERICAL ALGORITHMS | 2018年 / 79卷 / 02期

关键词：

Fractional diffusion equation; Tension spline; Stability; Convergence; DIFFERENCE SCHEME; SUB-DIFFUSION; TERM;

D O I：

10.1007/s11075-017-0447-1

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The numerical solution for a class of time fractional diffusion equation via tension spline is studied. Time fractional derivative is considered in the Caputo sense. The numerical method is constructed by means of the Crank-Nicolson method and is proven to be conditionally stable. Convergence analysis is also discussed by using the Fourier series method. Numerical evidences are given to prove the efficiency of the proposed method.

引用

页码：479 / 497

页数：19

共 20 条

[1]

Al-Shibani F., 2015, INT J COMPUT METHODS, V12, P1

[2]

[Anonymous], 2006, THEORY APPL FRACTION

[3]

[Anonymous], 1999, FRACTIONAL DIFFERENT

[4] On the new fractional derivative and application to nonlinear Fisher's reaction-diffusion equation [J].

Atangana, Abdon .

APPLIED MATHEMATICS AND COMPUTATION, 2016, 273 :948-956

[5] Numerical solution for the model of RLC circuit via the fractional derivative without singular kernel [J].

Atangana, Abdon ;

Jose Nieto, Juan .

ADVANCES IN MECHANICAL ENGINEERING, 2015, 7 (10) :1-7

[6]

Brociek R, 2014, IMPLICIT FINITE DIFF

[7] Galerkin finite element method for two-dimensional Riesz space fractional diffusion equations [J].

Bu, Weiping ;

Tang, Yifa ;

Yang, Jiye .

JOURNAL OF COMPUTATIONAL PHYSICS, 2014, 276 :26-38

[8] A Fourier method for the fractional diffusion equation describing sub-diffusion [J].

Chen, Chang-Ming ;

Liu, F. ;

Turner, I. ;

Anh, V. .

JOURNAL OF COMPUTATIONAL PHYSICS, 2007, 227 (02) :886-897

[9]

Guo B., 2015, Fractional Partial Differential Equations and their Numerical Solutions

[10] SOLVING THE TIME-FRACTIONAL DIFFUSION EQUATION USING A LIE GROUP INTEGRATOR [J].

Hashemi, Mir Sajjad ;

Baleanu, Dumitru ;

Parto-Haghighi, Mohammad ;

Darvishi, Elham .

THERMAL SCIENCE, 2015, 19 :S77-S83

← 1 2 →