Abstract:
In this paper a new Adomian decomposition method is presented by the authors for the numerical solutions of partial differential equations in 2 dimensions. They analysed numerical point of view of a relatively new numerical decomposition scheme for solving a linear Helmholtz equation model problem. The approach is based on the choice of a suitable differential operator which may be ordinary or partial, linear or nonlinear, deterministic or stochastic. It does not require discretization and consequently massive computation. In this scheme the solution is calculated in the form of a convergent power series with easily computable components. The paper particularly concerns a numerical comparison with Adomian decomposition and a conventional Finite-difference method. The numerical results demonstrate that the new method is quite accurate and readily implemented.
Page(s):
7-20
DOI:
DOI not available
Published:
Journal: Journal of Natural Sciences and mathematics, Volume: 42, Issue: 1, Year: 2002