Numerical solution of one-dimensional Burgers' equation using reproducing kernel function

By Shusen Xie, Sunyeong Heo, Seokchan Kim, G. Woo, Su-Cheol Yi. 2008

74 citations recorded by the source corpus.

This paper presents a numerical method for one-dimensional Burgers' equation by the Hopf-Cole transformation and a reproducing kernel function, abbreviated as RKF. The numerical solution is given as explicit integral expressions with the RKF at each time step, so that the computation is fully parallel. The stability and error estimates are derived. Numerical results for some test problems are presented and compared with the exact solutions. Some numerical results are also compared with the results obtained by other methods. The present method is easily implemented and effective.

View Paper: https://www.semanticscholar.org/paper/db4110531be9511e0501c37f7218c8530066bf72

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Citations in the corpus

• Shock wave simulations using Sinc Differential Quadrature Method (2011, methodology): “, 2005), reproducing kernel function method (Xie et al., 2007), the coupled linearized and rational methods with differential quadrature method (Wu and Wu, 2004), etc.”