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Computational and Applied Mathematics

, Volume 37, Issue 3, pp 2816–2836 | Cite as

\(L^{\infty }\) error bound of conservative compact difference scheme for the generalized symmetric regularized long-wave (GSRLW) equations

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Abstract

In this paper, we design a compact finite difference scheme which preserves the original conservative properties to solve the generalized symmetric regularized long-wave equations. The existence of the difference solution is proved by the Brouwer fixed-point theorem. Applying the discrete energy method, the convergence and stability of the difference scheme is obtained, and its numerical convergence order is \(O(\tau ^{2}+h^{4})\) in the \(L^{\infty }\)-norm for u and \(\rho \). For computing the nonlinear algebraic system generated by the compact scheme, a decoupled iterative algorithm is constructed and proved to be convergent. Numerical experiment results show that the theory is accurate and the method is efficient and reliable.

Keywords

Generalized SRLW equations Compact difference scheme Conservative Convergence in \(L^{\infty }\)-norm Iterative algorithm 

Mathematics Subject Classification

65M06 65M12 

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Copyright information

© SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2017

Authors and Affiliations

  1. 1.Computational Mathematics and Mathematical Physics DepartmentBauman Moscow State Technical UniversityMoscowRussia
  2. 2.College of Electrical and Electronic EngineeringHarbin University of Science and TechnologyHarbinChina

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