THE CRANK-NICOLSON TYPE COMPACT DIFFERENCE SCHEMES FOR A LOADED TIME-FRACTIONAL HALLAIRE EQUATION

被引：15

作者：

Alikhanov, Anatoly ^{[1
]}

Beshtokov, Murat G. ^{[2
]}

Mehra, Mani ^{[3
]}

机构：

[1] North Caucasus Fed Univ, North Caucasus Ctr Math Res, 1 Pushkina Str, Stavropol 355017, Russia

[2] Russian Acad Sci, Inst Appl Math & Automat, Kabardin Balkar Sci Ctr, 89A Shortanova Str, Nalchik 360000, Russia

[3] Indian Inst Technol Delhi, New Delhi 110016, India

来源：

FRACTIONAL CALCULUS AND APPLIED ANALYSIS | 2021年 / 24卷 / 04期

关键词：

Caputo fractional derivative; pseudoparabolic equation; Hallaire equation; compact finite difference schemes; scheme of Crank-Nicolson; stability; convergence of difference scheme; BOUNDARY-VALUE PROBLEM; DIFFUSION EQUATION; HEAT-EQUATION; PSEUDOPARABOLIC EQUATIONS; NUMERICAL-METHODS; VARIABLE-ORDER;

D O I：

10.1515/fca-2021-0053

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we study a loaded modified diffusion equation (the Hal-laire equation with the fractional derivative with respect to time). The compact finite difference schemes of Crank-Nicolson type of higher order is developed for approximating the stated problem on uniform grids with the orders of accuracy O(h(4) + tau(2-alpha)) and O(h(4) + tau(2)). A priori estimates are obtained for solutions of differential and difference equations. Stability of the suggested schemes and also their convergence with the rate equal to the order of the approximation error are proved. Proposed theoretical calculations are illustrated by numerical experiments on test problems.

引用

页码：1231 / 1256

页数：26

共 59 条

[1] Finite-difference methods for solving loaded parabolic equations [J].

Abdullayev, V. M. ;

Aida-zade, K. R. .

COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS, 2016, 56 (01) :93-105

[2] A priori estimates for solutions of boundary value problems for fractional-order equations [J].

Alikhanov, A. A. .

DIFFERENTIAL EQUATIONS, 2010, 46 (05) :660-666

[3] Boundary Value Problems for Certain Classes of Loaded Differential Equations and Solving Them by Finite Difference Methods [J].

Alikhanov, A. A. ;

Berezgov, A. M. ;

Shkhanukov-Lafishev, M. X. .

COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS, 2008, 48 (09) :1581-1590

[4] A Time-Fractional Diffusion Equation with Generalized Memory Kernel in Differential and Difference Settings with Smooth Solutions [J].

Alikhanov, Anatoly A. .

COMPUTATIONAL METHODS IN APPLIED MATHEMATICS, 2017, 17 (04) :647-660

[5] Numerical methods of solutions of boundary value problems for the multi-term variable-distributed order diffusion equation [J].

Alikhanov, Anatoly A. .

APPLIED MATHEMATICS AND COMPUTATION, 2015, 268 :12-22

[6] A new difference scheme for the time fractional diffusion equation [J].

Alikhanov, Anatoly A. .

JOURNAL OF COMPUTATIONAL PHYSICS, 2015, 280 :424-438

[7] Boundary value problems for the diffusion equation of the variable order in differential and difference settings [J].

Alikhanov, Anatoly A. .

APPLIED MATHEMATICS AND COMPUTATION, 2012, 219 (08) :3938-3946

[8]

[Anonymous], 1973, Stability of Finite Difference Schemes

[9] Locally One-Dimensional Difference Scheme for a Fractional Tracer Transport Equation [J].

Ashabokov, B. A. ;

Beshtokova, Z. V. ;

Shkhanukov-Lafishev, M. Kh .

COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS, 2017, 57 (09) :1498-1510

[10]

Barenblatt G. I., 1960, PMM-J APPL MATH MEC, V25, P852, DOI DOI 10.1016/0021-8928(60)90107-6

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