## Sinc numerical solution for solitons and solitary waves.(English)Zbl 1010.65043

Summary: A numerical scheme using the Sinc-Galerkin method is developed to approximate the solution for the Korteweg-de Vries model equation. Sinc approximation to both derivatives and indefinite integral reduce the integral equation to an explicit system of algebraic equations, then using various properties of Sinc functions, it is shown that the Sinc solution produce an error of order $$O(\exp(-c/h))$$ for some positive constants $$c$$, $$h$$. The method is applied to a few test examples to illustrate the accuracy and the implementation of the method.

### MSC:

 65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs 65M15 Error bounds for initial value and initial-boundary value problems involving PDEs 35Q53 KdV equations (Korteweg-de Vries equations) 35Q51 Soliton equations
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### References:

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