A method for calculating generalized solutions to the one-dimensional linear advection equation (Q2714086)
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scientific article; zbMATH DE number 1603344
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A method for calculating generalized solutions to the one-dimensional linear advection equation |
scientific article; zbMATH DE number 1603344 |
Statements
10 June 2001
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transport equation
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generalized solution
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finite-difference method
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higher-order approximation
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linear advection equation
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A method for calculating generalized solutions to the one-dimensional linear advection equation (English)
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The author develops a numerical method for calculating generalized solutions to the transport equation in the case of one-dimensional spatial variable. He constructs a class of numerical schemes which guarantee a higher-order approximation to generalized solutions for the transport equation. The construction of these schemes is based on expansion of the generalized solutions under consideration into the sum of smooth and singular parts. The advantage of the method suggested is that the schemes make it possible to avoid loss of accuracy which is inevitable for almost all methods in practice.
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