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A computational method for solving one-dimensional variable-coefficient Burgers equation. (English) Zbl 1118.35348

Summary: The Burgers equation is a simple one-dimensional model of the Navier-Stokes equation. In this paper, the exact solution to one-dimensional variable-coefficient Burgers equation is obtained in the reproducing kernel space \(W_{(2,3)}\). The exact solution is represented in the form of series. The \(n\)-term approximation \(u_{n}(t, x)\) is proved to converge to the exact solution \(u(t, x)\). Moreover, the approximate error of \(u_{n}(t, x)\) is monotone decreasing. Some numerical examples are studied to demonstrate the accuracy of the present method.

MSC:

35Q53 KdV equations (Korteweg-de Vries equations)
35C10 Series solutions to PDEs
35-04 Software, source code, etc. for problems pertaining to partial differential equations

Software:

Mathematica
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References:

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