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

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

Abstract and Applied Analysis, 2012, vol. 2012, issue 1

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.

Date: 2012
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https://doi.org/10.1155/2012/418943

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:418943

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