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2011•Journal of Sichuan UniversityRequires access

A new conservation finite difference scheme for generalized regularized long wave equation

Xu You

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Abstract

The numerical solution for an initial-boundary value problem of generalized regularized long wave equation is considered.An implicit pseudo-compact finite difference of two levels is proposed.This scheme simulates the conservation properties of the problem well.And the existence and uniqueness of the solution are also obtained.It is proved that the finite difference scheme is convergent with order 2 and stable without condition.The numerical examples show this scheme is feasible and its accuracy is better than usual difference scheme of two levels.

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What this paper is about

The numerical solution for an initial-boundary value problem of generalized regularized long wave equation is considered.An implicit pseudo-compact finite difference of two levels is proposed.This scheme simulates the conservation properties of the problem well.And the existence and uniqueness of the solution are also obtained.It is proved that the finite difference scheme is convergent with order 2 and stable without condition.The numerical examples show this scheme is feasible and its accuracy is better than usual difference scheme of two levels.

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Available abstract

The numerical solution for an initial-boundary value problem of generalized regularized long wave equation is considered.An implicit pseudo-compact finite difference of two levels is proposed.This scheme simulates the conservation properties of the problem well.And the existence and uniqueness of the solution are also obtained.It is proved that the finite difference scheme is convergent with order 2 and stable without condition.The numerical examples show this scheme is feasible and its accuracy is better than usual difference scheme of two levels.

Key concepts: Mathematics, Uniqueness, Finite difference coefficient, Finite difference scheme, Central differencing scheme, Finite difference method, Finite difference, Scheme (mathematics)

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