High accuracy cubic spline approximation on a geometric mesh for the solution of 1D non-linear wave equations
Abstract
In this paper, we propose a new high order three-level implicit compact discretization based on cubic spline approximation on a non-uniform mesh in space-direction for the solution of 1D non-linear hyperbolic partial differential equation of the form $u_{tt} = u_{tt} + G (x,t,u,u_x, u_t)$ subject to appropriate initial and Dirichlet boundary conditions. We use only three grid points at each time level and describe the derivation procedure in details. We also show how our method is able to handle the wave equation in polar coordinates. Numerical results are provided to justify the usefulness of the proposed method.
Copyright © 2012 Suruchi Singh, Swarn Singh, R. K. Mohanty. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Cite this article
S. Singh, S. Singh, R. K. Mohanty, High accuracy cubic spline approximation on a geometric mesh for the solution of 1D non-linear wave equations, J. Math. Comput. Sci. 2 (2012), 1126–1143.
BibTeX
@article{Singh2012,
author = {Singh, Suruchi and Singh, Swarn and Mohanty, R. K.},
title = {High accuracy cubic spline approximation on a geometric mesh for the solution of 1D non-linear wave equations},
journal = {J. Math. Comput. Sci.},
volume = {2},
year = {2012},
pages = {1126--1143},
doi = {}
}