The solution of a nonclassic problem for one-dimensional hyperbolic equation using the decomposition procedure
- 1 August 2004
- journal article
- other
- Published by Informa UK Limited in International Journal of Computer Mathematics
- Vol. 81 (8), 979-989
- https://doi.org/10.1080/00207160410001712297
Abstract
In this article, we propose a new approach for solving an initial–boundary value problem with a non-classic condition for the one-dimensional wave equation. Our approach depends mainly on Adomian's technique. We will deal here with new type of nonlocal boundary value problems that are the solution of hyperbolic partial differential equations with a non-standard boundary specification. The decomposition method of G. Adomian can be an effective scheme to obtain the analytical and approximate solutions. This new approach provides immediate and visible symbolic terms of analytic solution as well as numerical approximate solution to both linear and nonlinear problems without linearization. The Adomian's method establishes symbolic and approximate solutions by using the decomposition procedure. This technique is useful for obtaining both analytical and numerical approximations of linear and nonlinear differential equations and it is also quite straightforward to write computer code. In comparison to traditional procedures, the series-based technique of the Adomian decomposition technique is shown to evaluate solutions accurately and efficiently. The method is very reliable and effective that provides the solution in terms of rapid convergent series. Several examples are tested to support our study.Keywords
This publication has 21 references indexed in Scilit:
- T-complete functions for thin and thick plates on elastic foundationNumerical Methods for Partial Differential Equations, 2004
- A computational algebraic investigation of the decomposition method for time-dependent problemsApplied Mathematics and Computation, 2001
- An application of the decomposition method for second order wave equationsInternational Journal of Computer Mathematics, 2000
- A reliable modification of Adomian decomposition methodApplied Mathematics and Computation, 1999
- Decomposition methods: A new proof of convergenceMathematical and Computer Modelling, 1993
- Application of the decomposition method to the solution of the reaction-convection-diffusion equationApplied Mathematics and Computation, 1993
- New results for convergence of Adomian's method applied to integral equationsMathematical and Computer Modelling, 1992
- Solving parabolic integro-differential equations by an explicit integration methodJournal of Computational and Applied Mathematics, 1992
- A new approach to the wave equation—An application of the decomposition methodJournal of Mathematical Analysis and Applications, 1989
- Modification of the decomposition Approach to the Heat EquationJournal of Mathematical Analysis and Applications, 1987