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

✍ Scribed by Shu-Sen Xie; Sunyeong Heo; Seokchan Kim; Gyungsoo Woo; Sucheol Yi

Publisher
Elsevier Science
Year
2008
Tongue
English
Weight
900 KB
Volume
214
Category
Article
ISSN
0377-0427

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✦ Synopsis

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.

📜 SIMILAR VOLUMES

Numerical solutions of two-dimensional B
Numerical solutions of two-dimensional Burgers’ equations by discrete Adomian decomposition method
✍ Hongqing Zhu; Huazhong Shu; Meiyu Ding 📂 Article 📅 2010 🏛 Elsevier Science 🌐 English ⚖ 746 KB

In this paper, the discrete Adomian decomposition method (ADM) is proposed to numerically solve the two-dimensional Burgers' nonlinear difference equations. Two test problems are considered to illustrate the accuracy of the proposed discrete decomposition method. It is shown that the numerical resul