Asymptotic numerical method for singularly perturbed third order ordinary differential equations with a discontinuous source term. (English) Zbl 1164.65026

Valanarasu, T.; Ramanujam, T.

Novi Sad J. Math. 37, No. 2, 41-57 (2007).

A class of singularly perturbed two point boundary value problems (BVP) of reaction-diffusion type for third order ordinary differential equations (ODE) with a small positive parameter multiplying the highest derivative and a discontinuous source term is considered. The BVP is reduced to a weakly coupled system consisting of one first order ODE with a suitable initial condition and one second order singularly perturbed ODE subject to boundary conditions. In order to solve this system, a computational method is suggested. Examples are provided to illustrate the method.

Reviewer: Dejan Bojović (Kragujevac)

MSC:

65L10	Numerical solution of boundary value problems involving ordinary differential equations
34B15	Nonlinear boundary value problems for ordinary differential equations
34E15	Singular perturbations for ordinary differential equations

Keywords:

singularly perturbation; third order differential equation; asymptotic expansion approximation; numerical examples; two point boundary value problems; reaction-diffusion type; discontinuous source term