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A Jacobi Dual-Petrov Galerkin-Jacobi Collocation Method for Solving Korteweg-de Vries Equations

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  • Ali H. Bhrawy
  • M. M. Al-Shomrani

Abstract

The present paper is devoted to the development of a new scheme to solve the initial-boundary value Korteweg-de Vries equation which models many physical phenomena such as surface water waves in a channel. The scheme consists of Jacobi dual-Petrov Galerkin-Jacobi collocation method in space combined with Crank-Nicholson-leap-frog method in time such that at each time step only a sparse banded linear algebraic system needs to be solved. Numerical results are presented to show that the proposed numerical method is accurate and efficient for Korteweg-de Vries equations and other third-order nonlinear equations.

Suggested Citation

  • Ali H. Bhrawy & M. M. Al-Shomrani, 2012. "A Jacobi Dual-Petrov Galerkin-Jacobi Collocation Method for Solving Korteweg-de Vries Equations," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-16, September.
    • Handle: RePEc:hin:jnlaaa:418943
    DOI: 10.1155/2012/418943
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