\(L^ 1\) and \(L^{\infty}\) uniform convergence of a difference scheme for a semilinear singular perturbation problem (Q1077896)
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scientific article; zbMATH DE number 3958624
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | \(L^ 1\) and \(L^{\infty}\) uniform convergence of a difference scheme for a semilinear singular perturbation problem |
scientific article; zbMATH DE number 3958624 |
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\(L^ 1\) and \(L^{\infty}\) uniform convergence of a difference scheme for a semilinear singular perturbation problem (English)
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1987
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A nonlinear difference scheme is given for solving a semilinear singularly perturbed two-point boundary value problem. Without any restriction on turning points, the solution of the scheme is shown to be first order accurate in the discrete \(L^ 1\) norm, uniformly in the perturbation parameter. When turning points are excluded, the scheme is first order accurate in the discrete \(L^{\infty}\) norm, uniformly in the perturbation parameter.
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uniform convergence
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nonlinear difference scheme
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semilinear singularly perturbed two-point boundary value problem
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turning points
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0.9525453
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0.93567514
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0.9300244
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0.92993385
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0.92920625
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