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2014•Advances in Mathematical PhysicsOpen access

Two Conservative Difference Schemes for Rosenau-Kawahara Equation

Jinsong Hu, Youcai Xu, Bing Lin Hu, Xiaoping Xie

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Abstract

Two conservative finite difference schemes for the numerical solution of the initialboundary value problem of Rosenau-Kawahara equation are proposed. The difference schemes simulate two conservative quantities of the problem well. The existence and uniqueness of the difference solution are proved. It is shown that the finite difference schemes are of second-order convergence and unconditionally stable. Numerical experiments verify the theoretical results.

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What this paper is about

Two conservative finite difference schemes for the numerical solution of the initialboundary value problem of Rosenau-Kawahara equation are proposed. The difference schemes simulate two conservative quantities of the problem well. The existence and uniqueness of the difference solution are proved. It is shown that the finite difference schemes are of second-order convergence and unconditionally stable. Numerical experiments verify the theoretical results.

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Available abstract

Two conservative finite difference schemes for the numerical solution of the initialboundary value problem of Rosenau-Kawahara equation are proposed. The difference schemes simulate two conservative quantities of the problem well. The existence and uniqueness of the difference solution are proved. It is shown that the finite difference schemes are of second-order convergence and unconditionally stable. Numerical experiments verify the theoretical results.

Key concepts: Mathematics, Uniqueness, Finite difference method, Finite difference, Convergence (economics), Finite difference coefficient, Applied mathematics, Significant difference

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