HIGHER ORDER COMPACT FINITE DIFFERENCE METHOD FOR SINGULARLY PERTURBED ONE DIMENSIONAL REACTION DIFFUSION PROBLEMS

GEMECHIS FILE, FEYISA EDOSA

Abstract


In this paper, a higher order numerical method based on finite difference scheme with uniform mesh is presented for solving singularly perturbed two-point boundary value problems of reaction diffusion type. An eighth order compact finite difference has been developed for solving the problem. To demonstrate the efficiency of the method, three test examples have been considered. The numerical results obtained by the present method are tabulated and compared with some results of the previous findings of others existing in the literature. Graphs are also depicted in support of the numerical results. The convergence of the method has been examined and the theoretical error bound has been established. The present method is simple and it approximates the exact solution very well.

Full Text:

PDF

References


Natesan S, Ramanujam., Initial-value technique for singularly perturbed boundary value problems for second-order ordinary differential equations arising in chemical reactor theory. Journal of optimization theory and applications 97 (2) 455-470, 1998.

Farrell PA, Hegarty AF, Miller JJH, ORiordan E, and Shishkin GI., Robust computational techniques for boundary layers., Chapman & Hall/CRC Press; 2000.

Cole JD, Kevorkian J. , Perturbation Methods in Applied Mathematics., Springer, New York; 1979.

Bender CM, Orszag SA. , Advanced mathematical methods for scientist and engineers., Springer,McGraw-Hill, New York; 1978.

Eckhaus W. , Matched asymptotic expansions and singular perturbations. , North-Holland, Amsterdam; 1973.

Van Dyke M. , Perturbation methods in fluid mechanics. , Parabolic Press, Stanford, CA; 1975.

Bellman R. , Perturbation techniques in mathematics, physics and engineering., Holt, Rinehart & Winston, New York; 1964.

Bawa RK, Clavero C., Higher order global solution and normalized flux for singularly perturbed reaction-diffusion problems. Appl. Math. Comput. 2010; 216(7): 216 (7) 2058-2068, 2010.

Gasparo MG, Macconi M. , Numerical solution of second order nonlinear singularly perturbed boundary-value problems by initial value methods. Journal of Optimization Theory and Applications 1992; 73 309-327, 1992.


Refbacks

  • There are currently no refbacks.


Copyright (c) 2018 Journal of the Nigerian Mathematical Society

Creative Commons License
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.