## 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

Mathematica
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### References:

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