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2014 | 24 | 2 | 387-395
Tytuł artykułu

A robust computational technique for a system of singularly perturbed reaction-diffusion equations

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this paper, a singularly perturbed system of reaction-diffusion Boundary Value Problems (BVPs) is examined. To solve such a type of problems, a Modified Initial Value Technique (MIVT) is proposed on an appropriate piecewise uniform Shishkin mesh. The MIVT is shown to be of second order convergent (up to a logarithmic factor). Numerical results are presented which are in agreement with the theoretical results.
Rocznik
Tom
24
Numer
2
Strony
387-395
Opis fizyczny
Daty
wydano
2014
otrzymano
2013-03-07
poprawiono
2013-11-29
Twórcy
autor
  • School of Mathematics and Computer Applications, Thapar University, Patiala, 147004, India
  • Department of Computer Science, Punjabi University, Patiala 147002, India
  • School of Mathematics and Computer Applications, Thapar University, Patiala, 147004, India
Bibliografia
  • Bawa, R.K., Lal, A.K. and Kumar, V. (2011). An ϵ-uniform hybrid scheme for singularly perturbed delay differential equations, Applied Mathematics and Computation 217(21): 8216-8222.
  • Das, P. and Natesan, S. (2013). A uniformly convergent hybrid scheme for singularly perturbed system of reaction-diffusion Robin type boundary-value problems, Journal of Applied Mathematics and Computing 41(1): 447-471.
  • Doolan, E.P., Miller, J.J.H. and Schilders, W.H.A. (1980). Uniform Numerical Methods for Problems with Initial and Boundary Layers, Boole Press, Dublin.
  • Farrell, P.E., Hegarty, A.F., Miller, J.J.H., O'Riordan, E. and Shishkin, G.I. (2000). Robust Computational Techniques for Boundary Layers, Chapman & Hall/CRC Press, New York, NY.
  • Madden, N. and Stynes, M. (2003). A uniformly convergent numerical method for a coupled system of two singularly perturbed linear reaction-diffusion problems, IMA Journal of Numerical Analysis 23(4): 627-644.
  • Matthews, S., Miller, J.J.H., O'Riordan, E. and Shishkin, G.I. (2000). Parameter-robust numerical methods for a system of reaction-diffusion problems with boundary layers, in G.I. Shishkin, J.J.H. Miller and L. Vulkov (Eds.), Analytical and Numerical Methods for ConvectionDominated and Singularly Perturbed Problems, Nova Science Publishers, New York, NY, pp. 219-224.
  • Matthews, S., O'Riordan, E. and Shishkin, G.I. (2002). A numerical method for a system of singularly perturbed reaction-diffusion equations, Journal of Computational and Applied Mathematics 145(1): 151-166.
  • Melenk, J.M., Xenophontos, C. and Oberbroeckling, L. (2013). Analytic regularity for a singularly perturbed system of reaction-diffusion equations with multiple scales, Advances in Computational Mathematics 39(2): 367-394.
  • Miller, J.J.H., O'Riordan, E. and Shishkin, G.I. (1996). Fitted Numerical Methods for Singular Perturbation Problems, World Scientific, Singapore.
  • Natesan, S. and Briti, S.D. (2007). A robust computational method for singularly perturbed coupled system of reaction-diffusion boundary value problems, Applied Mathematics and Computation 188(1): 353-364.
  • Nayfeh, A.H. (1981). Introduction to Perturbation Methods, Wiley, New York, NY.
  • Rao, S.C.S., Kumar, S. and Kumar, M. (2011). Uniform global convergence of a hybrid scheme for singularly perturbed reaction-diffusion systems, Journal of Optimization Theory and Applications 151(2): 338-352.
  • Roos, H.-G., Stynes, M. and Tobiska, L. (1996). Numerical Methods for Singularly Perturbed Differential Equations, Springer, Berlin.
  • Shishkin, G.I. (1995). Mesh approximation of singularly perturbed boundary-value problems for systems of elliptic and parabolic equations, Computational Mathematics and Mathematical Physics 35(4): 429-446.
  • Sun, G. and Stynes, M. (1995). An almost fourth order uniformly convergent difference scheme for a semilinear singularly perturbed reaction-diffusion problem, Numerische Mathematik 70(4): 487-500.
  • Valanarasu, T. and Ramanujam, N. (2004). An asymptotic initial-value method for boundary value problems for a system of singularly perturbed second-order ordinary differential equations, Applied Mathematics and Computation 147(1): 227-240.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-amcv24i2p387bwm
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