A parameter-uniform numerical method for a Sobolev problem with initial layer |
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Authors: | G M Amiraliyev Hakki Duru I G Amiraliyeva |
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Institution: | (1) Faculty of Art and Science, Department of Mathematics, Yüzüncü Yıl University, 65080 Van, Turkey;(2) Faculty of Agriculture, Yüzüncü Yıl University, 65080 Van, Turkey |
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Abstract: | The present study is concerned with the numerical solution, using finite difference method of a one-dimensional initial-boundary
value problem for a linear Sobolev or pseudo-parabolic equation with initial jump. In order to obtain an efficient method,
to provide good approximations with independence of the perturbation parameter, we have developed a numerical method which
combines a finite difference spatial discretization on uniform mesh and the implicit rule on Shishkin mesh(S-mesh) for the
time variable. The fully discrete scheme is shown to be convergent of order two in space and of order one expect for a logarithmic
factor in time, uniformly in the singular perturbation parameter. Some numerical results confirming the expected behavior
of the method are shown.
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Keywords: | Uniform convergence Difference scheme Sobolev problem Singular perturbation S-mesh |
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