Improvement of numerical solution of self-adjoint singular perturbation problems by incorporation of asymptotic approximations (Q1294321)
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scientific article; zbMATH DE number 1311123
| Language | Label | Description | Also known as |
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| English | Improvement of numerical solution of self-adjoint singular perturbation problems by incorporation of asymptotic approximations |
scientific article; zbMATH DE number 1311123 |
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Improvement of numerical solution of self-adjoint singular perturbation problems by incorporation of asymptotic approximations (English)
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19 July 2000
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A numerical method for singularly perturbed two-point boundary value problems (BVPs) for second-order ordinary differential equations without a first derivative terms is proposed. Using the fundamental idea of the booster method by \textit{M. Israeli} and \textit{M. Ungarish} [Numer. Math. 39, 309-324 (1982; Zbl 0489.65054)], the authors solve the selfadjoint BVPs numerically and derive necessary error estimates. The numerical results illustrate the improvement of numerical solution. To study nonlinear problems the Newton quasi-linearization method is used.
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singular perturbation
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asymptotic approximation
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finite difference scheme
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numerical examples
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booster method
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error estimates
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nonlinear problems
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Newton quasi-linearization method
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