On the solution of boundary value problem. The decomposition method. (English) Zbl 0843.34026

Lee, E. S.; Adomian, G.

Bainov, D. (ed.) et al., Proceedings of the fourth international colloquium on differential equations, Plovdiv, Bulgaria, August 18-22, 1993. Utrecht: VSP. 163-166 (1994).

Summary: The method developed by Adomian, the decomposition method, supplies approximate solution to the original nonlinear and/or stochastic ordinary, partial, or integral differential equations. The approach may be used to find analytical approximations of the solution of the original equations. Since no linearization or perturbation is used and also since the solution can be approximated as close a needed, this approximate analytical solution forms a very useful tool for analyzing boundary value problems encountered in practice. It should be pointed out that these boundary value problems are usually unstable and very difficult to solve numerically. Furthermore, even for nonlinear problems without the consideration of the boundary value difficulties, linearization or perturbation approaches frequently alter the characteristics of the original problem completely. In this paper, we wish to show the difficulties in handling nonlinear boundary value problems and how the decomposition method can be used to analyze these type of problems.
For the entire collection see [Zbl 0835.00017].

MSC:

34B15

Nonlinear boundary value problems for ordinary differential equations

Keywords:

decomposition method; approximate analytical solution; nonlinear boundary value problems