A numerical method for first order nonlinear scalar conservation laws in one-dimension (Q1111344)
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scientific article; zbMATH DE number 4076510
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A numerical method for first order nonlinear scalar conservation laws in one-dimension |
scientific article; zbMATH DE number 4076510 |
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A numerical method for first order nonlinear scalar conservation laws in one-dimension (English)
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1988
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A numerical method for the following initial value problem for first order nonlinear scalar hyperbolic conservation law \(u_ t+f(u)_ x=0,\) \(u(x,0)=u_ 0(x)\) is proposed. The method is to approximate f by a piecewise linear function and the initial value by a piecewise constant function. It is proved to be applicable as a numerical method for a general flux function and a general initial value. The authors also point out that the error in this method is far smaller than in any other method and illustrate the method in an example.
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finite method
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numerical example
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first order nonlinear scalar hyperbolic conservation law
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flux function
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