Non-separable splines and numerical computation of evolution equations by the Galerkin methods

Authors:
Toshihide Ueno;Masami Okada
Affiliations:
Department of Mathematics, Tokyo Metropolitan University, Hachioji, Japan;Department of Mathematics, Tokyo Metropolitan University, Hachioji, Japan
Venue:
Journal of Computational and Applied Mathematics
Year:
2009

Citing 4
Cited 0

An introduction to wavelets

An introduction to wavelets
A dynamically adaptive multilevel wavelet collocation method for solving partial differential equations in a finite domain

Journal of Computational Physics
On the adaptive numerical solution of nonlinear partial differential equations in wavelet bases

Journal of Computational Physics
A finite difference method for the Korteweg-de Vries and the Kadomtsev-Petviashvili equations

Journal of Computational and Applied Mathematics

Quantified Score

Hi-index	7.29

Visualization

Abstract

We construct new non-separable splines and we apply the spline sampling approximation to the computation of numerical solutions of evolution equations. The non-separable splines are basis functions which give a fine sampling approximation which enables us to compute numerical solutions by means of the method of lines combined with the Galerkin method. To demonstrate our approach we compute numerical solutions of the Burgers equation and the Kadomtsev-Petviashvili equation.