A Successive Linearization Method Approach to Solve Lane-Emden Type of Equations

We propose a new application of the successive linearization method for solving singular initial and boundary value problems of Lane-Emden type. To demonstrate the reliability of the proposed method, a comparison is made with results from existing methods in the literature and with exact analytical solutions. It was found that the method is easy to implement, yields accurate results, and performs better than some numerical methods

Solution of a Subclass of Lane-Emden Differential Equation by Variational Iteration Method

In this paper we apply He's variational iteration method to find out an appropriate solution to a class of singular differential equation under imposed conditions by introducing and inducting in a polynomial pro satisfying the given subject to conditions at the outset as selective function to the solution extracting process. As for as application part is concerned, Illustrative examples from the available literature when treated all over reveal and out show that the solution deduced by proposed method is exact and again polynomial. Overall, a successful produce of exact solutions by proposed process itself justify the effectiveness and efficiency of the method so very much. Keywords: He's variational iteration method, Lane-Emden differential equation, exact solution, polynomial, Lagrange multiplier

Solution of a Subclass of Singular Second Order Differential Equation of Lane Emden type by Taylor Series Method

In this paper, a subclass of second order differential equation of Lane Emden type followed by imposed initial or boundary condition is identified for solving by Taylor's series method. Such types of problems come into existence while modeling upon some of peer physical phenomenon. The proposed method eventually produces an analytic solution in the form of a polynomial function. Again some of the problems available in literature are also considered and tested for solution to justify the suitability and viability of the method. Keywords: Variation iteration method, boundary value problems, analytic solution, Lane-Emden equation, He's Polynomial, Taylor series

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

A new approach for solving nonlinear singular boundary value problems

In this paper, an e_cient method based on Quasi-Newton's method and the simpli_ed reproducing kernel method is proposed for solving nonlinear singular boundary value problems. For the Quasi-Newton's method the convergence order is studied. The uniform convergence of the numerical solution as well as its derivatives are also proved. Numerical examples are given to demonstrate the e_ciency and stability of the proposed method. The numerical results are compared with exact solutions and the outcomes of other existing numerical methods