An Integral Transform-Weighted Residual Method for Solving Second Order Linear Boundary Value Differential Equations with Semi-Infinite Domain

Abstract

Solving boundary value problem with semi-infinite domain in a conventional way or using some of the available approximate methods poses a lot of challenges or better still seems almost impossible over the years, and some of the alternative ways for crossing this hurdle is by fixing value for infinity that is in the domain. Here in this work, we present an Integral Transform (Aboodh Transform) - Weighted Residual Based Method (AT-WRM) to address the afore-mentioned challenge. Aboodh Transform was used to transform and at the same time used to find the inverse of the given differential equations while Weighted Residual via Collocation Method was used in order to avoid fixing value for infinity as usual by introducing e^-ix in trial function to decay the infinity that was part of the boundary condition. The accuracy of the presented method was authenticated by solving three different problems. The excellent results obtained from the three solved problems validate the accuracy and effectiveness of the method