Nonlinear and Linear Conservative Finite Difference Schemes for Regularized Long Wave Equation
Koide, Satoshi ; Furihata, Daisuke
Japan J. Indust. Appl. Math., Tome 26 (2009) no. 1, p. 15-40 / Harvested from Project Euclid
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We propose four conservative schemes for the regularized long-wave (RLW) equation. The RLW equation has three invariants: mass, momentum, and energy. Our schemes are designed by using the discrete variational derivative method to inherit appropriate conservation properties from the equation. Two of our schemes conserve mass and momentum, while the other two schemes conserve mass and energy. With one of our schemes, we prove the numerical solution stability, the existence of the solutions, and the convergence of the solutions. Through some numerical computation examples, we demonstrate the efficiency and robustness of our schemes.
Publié le : 2009-02-15
Classification:  finite difference method,  discrete conservation laws,  nonlinear and linear schemes,  RLW equation 
@article{1244209204,
     author = {Koide, Satoshi and Furihata, Daisuke},
     title = {Nonlinear and Linear Conservative Finite Difference Schemes for Regularized Long Wave Equation},
     journal = {Japan J. Indust. Appl. Math.},
     volume = {26},
     number = {1},
     year = {2009},
     pages = { 15-40},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1244209204}
}

Koide, Satoshi; Furihata, Daisuke. Nonlinear and Linear Conservative Finite Difference Schemes for Regularized Long Wave Equation. Japan J. Indust. Appl. Math., Tome 26 (2009) no. 1, pp.  15-40. http://gdmltest.u-ga.fr/item/1244209204/