DİFÜZYON DENKLEMİNİN SINIRLAYICI TAYLOR YAKLAŞIMI YARDIMIYLA NÜMERİK ÇÖZÜMÜ

Year 2013, Issue: 030, 9 - 15, 15.04.2013

Ahmet Boz

Abstract

Bu çalışmada, lineer difüzyon denkleminin sınırlayıcı Taylor yaklaşımı yardımıyla nümerik çözümleri

elde edilmiştir. Difüzyon denkleminin nümerik çözümü için exp(xA) üstel matris yaklaşımı

kullanılmıştır. Bu yaklaşımın avantajı, bazı noktalarda denklemin tam değerine sahip olmasıdır. Difüzyon

denklemi için uygulanan yöntem sonucunda elde edilen veriler, yöntemin tutarlı olduğunu

göstermektedir.

Keywords

Sınırlayıcı Taylor yaklaşımı, Difüzyon denklemi, sonlu farklar

NUMERICAL SOLUTION OF THE DIFFUSION EQUATION WITH RESTRICTIVE TAYLOR APPROXIMATION

Abstract

In this paper, we solved linear diffusion equation using restrictive Taylor approximations. We use the

restrictive Taylor approximation to approximate the exponential matrix exp(xA) . The adventage is that

has the exact value at certain point. We will use a new technique for solution of the Diffusion equation.

The results show that the used numerical method produce the good results.

Keywords

Restrictive Taylor approximation, Diffusion equation, Finite difference

References

• [1] H.N.A. Ismail, E.M.E. Elbarbary, Highly accurate method for the convection–diffusion equation, Int. J. Comput. Math. 72 (1999) 271–280.
• [2] H.N.A. Ismail, E.M.E. Elbarbary, A.Y. Hassan, Highly accurate method for solving initial boundary value problem for first order hyperbolic differential equation, Int. J. Comput. Math. 77 (2000) 251–261.
• [3] H.N.A. Ismail, E.M.E. Elbarbary, Restrictive Taylor approximation and parabolic partial differential equations, Int. J. Comput. Math. 78 (2001) 73–82.
• [4] H.N.A. Ismail Unique solvability of restrictive Pade and restrictive Taylors approximations, Applied Mathematics and Computation, Volume 152, Issue 1, 26 April 2004, Pages 89-97
• [5] G. Gurarslan, M. Sari, Numerical solutions of linear and nonlinear diffusion equations by a differential quadrature method (DQM), Int. J. Numer. Meth. Biomed. Engng. 27,(2011), 69–77
• [6] G. Meral, M. Tezer-Sezgin, Differential quadrature solution of nonlinear reaction-diffusion equation with relaxation-type time integration, Int. J.Comput. Math. 86 (3) (2009) 451–463.
• [7] G. Meral, M. Tezer-Sezgin, The differential quadrature solution of nonlinear reaction-diffusion and wave equations using several time-integration schemes, Int. J. Numer. Meth. Biomed. Engng. 27,(2011), 461-632
• [8] G. Gurarslan ,Numerical modelling of linear and nonlinear diffusion equations by compact finite difference method Applied Mathematics and Computation 216 (2010) 2472–2478
• [9] Abdul-Majid Wazwaz, The variational iteration method: A powerfull scheme for handling linear and nonlinear diffusion equations, Computers and Mathematics with Applications 54,(2007) 933-939