A Shishkin mesh for a singularly perturbed Riccati equation (Q557775)
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scientific article; zbMATH DE number 2184027
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A Shishkin mesh for a singularly perturbed Riccati equation |
scientific article; zbMATH DE number 2184027 |
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A Shishkin mesh for a singularly perturbed Riccati equation (English)
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30 June 2005
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The paper deals with the singularly perturbed initial value problem \((\varepsilon u'+a(u^2-g^2))(x)=0\), \(x>0\), \(u(0)=A\), where \(a,g\in C^1[0,L)\) and \(\varepsilon >0\) is a small parameter. Bounds on the solution and its derivatives are derived. A numerical method for solving the equation is proposed based on a Shiskin mesh and error bounds for the numerical approximation are established.
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Singular perturbation
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Riccati equation
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Shishkin mesh
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initial value problem
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error bounds
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