Numerical solution of one-dimensional Burgers’ equation using reproducing kernel function. (English) Zbl 1140.65069

Xie, Shu-Sen; Heo, Sunyeong; Kim, Seokchan; Woo, Gyungsoo; Yi, Sucheol

J. Comput. Appl. Math. 214, No. 2, 417-434 (2008).

This paper present a numerical solution for the one-dimensional Burgers equation using a reproducing kernel function. The numerical solution and experiments are quite interesting. The convergence and stability are compared with the exact solutions. It is also shown that the results obtained can be easily implemented and are quite effective.

Reviewer: Aniket Mahanti (Saint John)

MSC:

65M60	Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
35Q53	KdV equations (Korteweg-de Vries equations)
65M12	Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
65M15	Error bounds for initial value and initial-boundary value problems involving PDEs
46E22	Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces)

Keywords:

Burgers equation; reproducing kernel function; error estimates; numerical examples; Hopf-Cole transformation; convergence; stability

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