A 6TH ORDER SPLINE PROCEDURE FOR A CLASS OF NONLINEAR BOUNDARY-VALUE-PROBLEMS

We consider a class of nonlinear boundary value problems of the form y'' + f(x, y) = 0, 0 less-than-or-equal-to x less-than-or-equal-to 1, subject to boundary conditions y(0) = alpha, and y(1) = beta. A numerical procedure is presented based on spline functions of degree five and six. Detailed error analysis and sixth order convergence of the scheme are discussed. Finally, computational efficiency and the convergence order are verified through numerical examples. For the sake of comparison, results using some well-known methods are also tabulated.