A new wavelet method for solving the Helmholtz equation with complex solution |
| |
| Authors: | M H Heydari M R Hooshmandasl F M Maalek Ghaini M Fatehi Marji R Dehghan M H Memarian |
| |
| Affiliation: | 1. Faculty of Mathematics, Yazd University, Yazd, Iran;2. The Laboratory of Quantum Information Processing, Yazd University, Yazd, Iran;3. Department of Mine Exploitation Engineering, Faculty of Mining and Metallurgy, Yazd University, Yazd, Iran;4. Faculty of Physics, Yazd University, Yazd, Iran |
| |
| Abstract: | The Helmholtz equation which is very important in a variety of applications, such as acoustic cavity and radiation wave, has been greatly considered in recent years. In this article, we propose a new efficient computational method based on the Legendre wavelets (LWs) expansion together with their operational matrices of integration and differentiation to solve this equation with complex solution. Because of the fact that both of the operational matrices of integration and differentiation are used in the proposed method, the boundary conditions are taken into account automatically. The main characteristic behind this approach is that it reduces such problems to those of solving a system of algebraic equations which greatly simplifies the problems. As an applied example, “propagation of plane waves” is investigated to demonstrate the validity and applicability of the presented method. © 2015 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 32: 741–756, 2016 |
| |
| Keywords: | derivative operational matrix Helmholtz equation integration operational matrix Legendre wavelets propagation of plane waves |
|
|
