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Title: Uniform Numerical Method For a Class of Parameterized Singularly Perturbed Problems
Authors: Mohapatra, J
Keywords: Singular perturbation
Parameterized problem
Boundary layer
Adaptive mesh
Uniform convergence
Issue Date: Dec-2014
Citation: International conference on Mathematical modeling and computer simulation, 8-10 December 2014, IIT Madras
Abstract: In this paper, we consider a quasi-linear first order singularly perturbed boundary value problem depending on a parameter. The problem is discretized by a backward Euler finite difference scheme on an appropriate non-uniform mesh constructed adaptively by equidistributing a positive monitor function based on the solution. We show that the proposed method is first order convergent whose error constants are shown to be independent of the singular perturbation parameter. Further, the proposed method is extended to problems with mixed type boundary conditions. A numerical example is solved using the presented method to support the result of convergence proved theoretically.
Description: Copyright belongs to proceeding publisher
Appears in Collections:Conference Papers

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