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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-like (Korteweg-de Vries) equations 35C10 Series solutions of PDE 35-04 Machine computation, programs (partial differential equations)
Mathematica
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