×

zbMATH — the first resource for mathematics

Two conservative difference schemes for the generalized Rosenau equation. (English) Zbl 1187.65090
Summary: Numerical solutions for generalized Rosenau equation are considered and two energy conservative finite difference schemes are proposed. Existence of the solutions for the difference scheme is shown. Stability, convergence, and priori error estimate of the scheme are proved using the energy method. Numerical results demonstrate that the two schemes are efficient and reliable.

MSC:
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35Q35 PDEs in connection with fluid mechanics
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
PDF BibTeX XML Cite
Full Text: DOI EuDML
References:
[1] Rosenau, P, Dynamics of dense discrete systems, Progress of Theoretical Physics, 79, 1028-1042, (1988)
[2] Park, MA, On the rosenau equation, Matematica Aplicada e Computacional, 9, 145-152, (1990) · Zbl 0723.35071
[3] Chung, SK; Pani, AK, Numerical methods for the rosenau equation, Applicable Analysis, 77, 351-369, (2001) · Zbl 1021.65048
[4] Choo, SM; Chung, SK; Kim, KI, A discontinuous Galerkin method for the rosenau equation, Applied Numerical Mathematics, 58, 783-799, (2008) · Zbl 1145.65071
[5] Manickam, SA; Pani, AK; Chung, SK, A second-order splitting combined with orthogonal cubic spline collocation method for the rosenau equation, Numerical Methods for Partial Differential Equations, 14, 695-716, (1998) · Zbl 0930.65111
[6] Chung, SK, Finite difference approximate solutions for the rosenau equation, Applicable Analysis, 69, 149-156, (1998) · Zbl 0904.65093
[7] Omrani, K; Abidi, F; Achouri, T; Khiari, N, A new conservative finite difference scheme for the rosenau equation, Applied Mathematics and Computation, 201, 35-43, (2008) · Zbl 1156.65078
[8] Hu, B; Xu, Y; Hu, J, Crank-Nicolson finite difference scheme for the rosenau-Burgers equation, Applied Mathematics and Computation, 204, 311-316, (2008) · Zbl 1166.65041
[9] Browder, FE, Existence and uniqueness theorems for solutions of nonlinear boundary value problems, Proceedings of Symposia in Applied Mathematics, 17, 24-49, (1965)
[10] Zhou Y: Applications of Discrete Functional Analysis to the Finite Difference Method. International Academic Publishers, Beijing, China; 1991:vi+260. · Zbl 0732.65080
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.