Solution of a broad Class Singular Boundary Value Problem by Variational Iteration Method

In this paper an iterative method for finding a compatible solution to a class of singular second order differential equation of prescribed boundary values often observed common is considered by constructing a successive sequence of correction functional via variational theory. The analytical convergence of such iteratively generated sequential scheme is analyzed explicitly and duly discussed.  Interestingly, the proposed method when applied on, over hither to widely quote numerical problems turns out to be quite encouraging and renders appropriate solution. May sometimes by this method the limiting value of functional sequence happens to be an exact solution too. Keywords; singular problem, Variational iteration method, Convergence, sequence, smooth function Lagrange multiplier, linearization, discretization, transformation

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

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 grou