Method of Weighted Residuals as Applied to Higher Order, Nonlinear, Two-Point Boundary Value Problems

A new numerical method for solving a class of higher order nonlinear two-point boundary value problems is presented. The present paper is an extension of an earlier work where only second order problems were addressed. This iterative technique first linearizes the problem by an initial guess for the nonlinear terms. The linearized boundary value problem is transformed into an initial value problem by using a weighted residuals technique. The resulting initial value problem is then solved by utilizing a fourth order Runge—Kutta scheme. The new solution generated is used as an improved estimate and the process iterated until a desired level of convergence is attained. Numerical solutions for third and fourth order problems are included.