A numerical scheme for diffusion-convection equation with piecewise constant arguments

被引：7

作者：

Esmailzadeh, Mojgan ^{[1
]}

Najafi, Hashem Saberi ^{[2
]}

Aminikhah, Hossein ^{[3
]}

机构：

[1] Islamic Azad Univ, Dept Appl Math, Lahijan Branch, Lahijan, Iran

[2] Islamic Azad Univ, Dept Math, Lahijan Branch, Lahijan, Iran

[3] Univ Guilan, Fac Math Sci, Dept Appl Math & Comp Sci, Rasht, Iran

来源：

COMPUTATIONAL METHODS FOR DIFFERENTIAL EQUATIONS | 2020年 / 8卷 / 03期

关键词：

Diffusion-convection equation; Piecewise constant arguments; theta-methods; Asymptotically stability; DIFFERENTIAL-EQUATIONS; THETA-METHODS; STABILITY;

D O I：

10.22034/cmde.2020.31155.1468

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This article is concerned with using a finite difference method, namely the.-methods, to solve the diffusion-convection equation with piecewise constant arguments.The stability of this scheme is also obtained. Since there are not many published results on the numerical solution of this sort of differential equation and because of the importance of the above equation in the physics and engineering sciences, we have decided to study and present a stable numerical solution for the above mentioned problem. At the end of article some experiments are done to demonstrate the stability of the scheme. We also draw the figures for the numerical and analytical solutions which confirm our results.The numerical solutions have also been compared with analytical solutions.

引用

页码：573 / 584

页数：12

共 18 条

[1] RETARDED DIFFERENTIAL-EQUATIONS WITH PIECEWISE CONSTANT DELAYS [J].

COOKE, KL ;

WIENER, J .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1984, 99 (01) :265-297

[2] Numerical solution of the three-dimensional advection-diffusion equation [J].

Dehghan, M .

APPLIED MATHEMATICS AND COMPUTATION, 2004, 150 (01) :5-19

[3] Weighted finite difference techniques for the one-dimensional advection-diffusion equation [J].

Dehghan, M .

APPLIED MATHEMATICS AND COMPUTATION, 2004, 147 (02) :307-319

[4] Stability of θ-schemes in the numerical solution of a partial differential equation with piecewise continuous arguments [J].

Liang, Hui ;

Liu, M. Z. ;

Lv, Wanjin .

APPLIED MATHEMATICS LETTERS, 2010, 23 (02) :198-206

[5] THE STABILITY OF THE THETA-METHODS IN THE NUMERICAL-SOLUTION OF DELAY DIFFERENTIAL-EQUATIONS [J].

LIU, MZ ;

SPIJKER, MN .

IMA JOURNAL OF NUMERICAL ANALYSIS, 1990, 10 (01) :31-48

[6] High-order compact solution of the one-dimensional heat and advection-diffusion equations [J].

Mohebbi, Akbar ;

Dehghan, Mehdi .

APPLIED MATHEMATICAL MODELLING, 2010, 34 (10) :3071-3084

[7]

Poorkarimi H., 2001, CONF, V07, P99

[8]

Poorkarimi H., 1999, Proceedings of the 15th Annual Conference of Applied Mathematics (Edman, OK), V2, P87

[9]

Shah S.M., 1983, Int. J. Math. Math. Sci., V6, P671, DOI [10.1155/S0161171283000599, DOI 10.1155/S0161171283000599]

[10] Stability of θ-methods for advanced differential equations with piecewise continuous arguments [J].

Song, MH ;

Yang, ZW ;

Liu, MZ .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2005, 49 (9-10) :1295-1301

← 1 2 →