Parameter-uniform numerical method for global solution and global normalized flux of singularly perturbed boundary value problems using grid equidistribution

Authors:
Jugal Mohapatra;Srinivasan Natesan
Affiliations:
Institute of Mathematics and Applications, Bhubaneswar - 751003, India;Department of Mathematics, Indian Institute of Technology Guwahati, Guwahati - 781 039, India
Venue:
Computers & Mathematics with Applications
Year:
2010

Citing 3
Cited 0

On the approximation of derivatives of singularly perturbed boundary value problems

SIAM Journal on Scientific and Statistical Computing
Numerical solution of a singularly perturbed two-point boundary value problem using equidistribution: analysis of convergence

Journal of Computational and Applied Mathematics
Approximation of derivatives in a convection-diffusion two-point boundary value problem

Applied Numerical Mathematics

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Abstract

In this paper, we present the analysis of an upwind scheme for obtaining the global solution and the normalized flux for a convection-diffusion two-point boundary value problem. The solution of the upwind scheme is obtained on a suitable nonuniform mesh which is formed by equidistributing the arc-length monitor function. It is shown that the discrete solution obtained by the upwind scheme and the global solution obtained via interpolation converges uniformly with respect to the perturbation parameter. In addition, we prove the uniform first-order convergence of the weighted derivative of the numerical solution on this nonuniform mesh and the uniform convergence of the global normalized flux on the whole domain. Numerical results are presented that demonstrate the sharpness of our results.