Wavelet Galerkin schemes for higher order time dependent partial differential equations
Gopal Priyadarshi, B. V. Rathish Kumar · Numerical Methods for Partial Differential Equations · 2018
Fourth‐order derivatives appearing in different linear and nonlinear transient higher order multidimensional equations modeling several physical problems have always posed computational challenges to widely prevailing numerical approaches such as FDM, FEM, and so forth. In this study, we address the issue effectively using the special features of Daubechies wavelets such as orthogonality, compact support, arbitrary regularity, high‐order vanishing moments, and good localization. An efficient compression strategy is proposed to reduce the computational cost significantly. Implicitly stable backward Euler scheme is used for time marching the evolving solution. A priori error estimates have been derived to prove the convergence of the numerical scheme. The proposed approach is successfully tested on few linear and nonlinear multidimensional PDEs.