Computational Solution of Two- Point Boundary Value Problem by Quadrature method in terms of Liouville-Green Transformation

Abstract

In this research paper we are selected a two-pointedge value problem ofsingular perturbation with Dirichlet type of margin conditions. The selected differential equation is transformedinto to the required form by using a Liouville –Green transformation. Then the computational process has been implemented for solving thetwo-pointborder line value problem ofsingular perturbation with either right or left end frontier layer in the specific interval [0,1]. The transformation reduces the mathematical complexity with some assumptions and applied numerical integration method to get the computations for different choices of the perturbation parameter,which is very near to zero. In the present research problem, we have observed the uniform convergence in the computational solution in the regular region and some chaotic behavior near the periphery layer region. We are implemented this method for several linear differential equations and observed that the numerically obtained resultsare validated with literature