New unconditionally stable scheme for telegraph equation based on weighted Laguerre polynomials |
| |
| Authors: | Di Zhang Xiaoping Miao |
| |
| Affiliation: | College of Defense Engineering, PLA University of Science and Technology, Nanjing, China |
| |
| Abstract: | This article proposes a new unconditionally stable scheme to solve one‐dimensional telegraph equation using weighted Laguerre polynomials. Unlike other numerical schemes, the time derivatives in the equation can be expanded analytically based on the Laguerre polynomials and basis functions. By applying a Galerkin temporal testing procedure and using the orthogonal property of weighted Laguerre polynomials, the time variable can be eliminated from computations, which results in an implicit equation. After solving the equation recursively one can obtain the numerical results of telegraph equation by using the expanded coefficients. Some numerical examples are considered to validate the accuracy and stability of this proposed scheme, and the results are compared with some existing numerical schemes.© 2017 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 1603–1615, 2017 |
| |
| Keywords: | telegraph equation weighted Laguerre polynomials unconditionally stable scheme |
|
|
