Initial value method for general singular perturbation problems

International Conference on Vibration Problems

Pavani, Loka^1

Department of Mathematics, OUCW, Koti, O.U., T.S., India^1

关键词: Exact solution;    First order equations;    First order problems;    Initial-value method;    Numerical results;    Numerical solution;    Second order problem;    Singular perturbation problems;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/662/1/012027/pdf
DOI  :  10.1088/1742-6596/662/1/012027

来源: IOP

【 摘 要 】

In general, the numerical solution of a boundary value problem will be more difficult than the numerical solution of the corresponding initial value problem. Hence, we prefer to convert the given second order problem into a first order problem. In this paper we present an initial value method. It is distinguished by the following fact: the original second order problem is replaced by an asymptotically equivalent first order problem and then solved as an initial value problem. Classical RungeKutta method is used to solve the first order equation. The method is first described for solving problems with left end boundary layer. This is extended for solving singular perturbation problems with right end, internal and terminal layers. We solve one problem to demonstrate the applicability of the method. The numerical results are compared with the exact solution.