Solution of a Singular Class of Boundary Value Problems by Variation Iteration Method

Abstract

In this paper, an effective methodology for finding solution to a general class of singular second order linear as well as nonlinear boundary value problems is proposed. These types of problems commonly occur in physical problems. The solution is developed by constructing a sequence of correctional functional via variation Iteration theory. The analytical convergence of such occurring sequences befitting to the context of the class of such existing problems is also discussed. The efficacy of the proposed method is tested on various problems. It is also observed that execution of only few successive iterations of correction functionals may lead to a solution that is either exact solution or very close to the exact solution.

Keywords: Variation iteration method, sequence, linearization, discretization, transformation Convergence, Lagrange multiplier, smooth function, B-Spline, projection method, Lie group