Solving a partially singularly perturbed initial value problem on Shishkin meshes |
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Authors: | P Maragatha Meenakshi S Valarmathi |
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Institution: | a Department of Mathematics, Periyar E.V.R College, Tiruchirappalli 620 017, Tamil Nadu, India b Department of Mathematics, Bishop Heber College, Tiruchirappalli 620 023, Tamil Nadu, India c Institute for Numerical Computation and Analysis, Dublin, Ireland |
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Abstract: | A coupled first order system of one singularly perturbed and one non-perturbed ordinary differential equation with prescribed initial conditions is considered. A Shishkin piecewise uniform mesh is constructed and used, in conjunction with a classical finite difference operator, to form a new numerical method for solving this problem. It is proved that the numerical approximations generated by this method are essentially first order convergent in the maximum norm at all points of the domain, uniformly with respect to the singular perturbation parameter. Numerical results are presented in support of the theory. |
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Keywords: | System of differential equations Initial value problem Singular perturbation problem Initial layer Classical finite difference scheme Fitted mesh |
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