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Parameter-uniform numerical methods for singularly perturbed mixed boundary value problems using grid equidistribution
Authors:Jugal Mohapatra  Srinivasan Natesan
Institution:1. Department of Mathematics, Indian Institute of Technology Guwahati, 781 039, Guwahati, India
Abstract:In this paper, we present the analysis of an upwind scheme for obtaining the solution of a convection-diffusion two-point boundary value problem with Robin boundary conditions. The solution 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 converges uniformly with respect to the perturbation parameter. Numerical results are presented that demonstrate the sharpness of the theoretical estimates.
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