publication . Preprint . 2018

Optimal error estimate of two linear and momentum-preserving Fourier pseudo-spectral schemes for the RLW equation

Hong, Qi; Wang, Yushun; Gong, Yuezheng;
Open Access English
  • Published: 25 Jun 2018
In this paper, two novel linear-implicit and momentum-preserving Fourier pseudo-spectral schemes are proposed and analyzed for the regularized long-wave equation. The numerical methods are based on the blend of the Fourier pseudo-spectral method in space and the linear-implicit Crank-Nicolson method or the leap-frog scheme in time. The two fully discrete linear schemes are shown to possess the discrete momentum conservation law, and the linear systems resulting from the schemes are proved uniquely solvable. Due to the momentum conservative property of the proposed schemes, the Fourier pseudo-spectral solution is proved to be bounded in the discrete $L^{\infty}$ ...
free text keywords: Mathematics - Numerical Analysis
Download from
41 references, page 1 of 3

1. Akbari, R., Mokhtari, R.: A new compact finite difference method for solving the generalized long wave equation. Numer. Funct. Anal. Optim. 35, 133-152 (2014)

2. Avrin, J., Goldstein, J.: Global existence for the Benjamin-Bona-Mahony equation in arbitrary dimensions. Nonlinear Anal. 9, 861-865 (1985) [OpenAIRE]

3. Benjamin, T., Bona, J., Mahony, J.: Model equations for long waves in nonlinear dispersive systems. Philos. Trans. R Soc. Lond. A 227, 47-78 (1972)

4. Bridges, T., Reich, S.: Multi-symplectic integrators: numerical schemes for Hamiltonian PDEs that conserve symplecticity. Phys. Lett. A. 284, 184-193 (2001)

5. Bubb, C., Piggot, M.: Geometric Integration and Its Application, Handbook of Numerical Analysis, vol. XI. NorthHolland, Amsterdam (2003)

6. Cai, J.: Multi-symplectic numerical method for the regularized long-wave equation. Comput. Phys. Commun. 180, 1821-1831 (2009)

7. Cai, J.: A new explicit multi-symplectic scheme for the regularized long-wave equation. J. Math. Phys. 50, 013535 (2009)

8. Cai, J., Gong, Y., Liang, H.: Novel implicit/explicit local conservative scheme for the regularized long-wave equation and convergence analysis. J. Math. Anal. Appl. 447, 17-31 (2017)

9. Cai J.X. Hong, Q.: Efficient local structure-preserving schemes for the RLW-Type equation. Numer. Methods Partial Differential Equations 33, 1678-1691 (2017)

10. Canuto, C., Quarteroni, A.: Approximation results for orthogonal polynomials in sobolev spaces,. Math. Comput. 38, 67-86 (1982) [OpenAIRE]

11. Chen, J., Qin, M.: Multi-symplectic Fourier pseudo-spectral method for the nonlinear Schrodinger equation. Electr. Trans. Numer. Anal. 12, 193-204 (2001)

12. Dag, I., Saka, B., Irk, D.: Application of cubic B-splines for numerical solution of the RLW equation. Appl. Math. Comput. 159, 373-389 (2004)

13. Dag, L.: Least-squares quadratic b-spline finite element method for the regularized long wave equation. Comput. Methods Mech. Engng. 182, 205-215 (2000)

14. Djidjeli, K., Price, G., Twizell, E., Cao, Q.: A linearized implicit pseudo-spectral method for some model equations-the regularized long wave equations. Commun. Numer. Meth. Engng. 19, 847-863 (2003)

15. Dogan, A.: Numerical solution of RLW equation using linear finite elements within Galerkin's method. Appl. Math. Model. 26, 771-783 (2002)

41 references, page 1 of 3
Powered by OpenAIRE Open Research Graph
Any information missing or wrong?Report an Issue