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, s ubject to boundary conditions y(0) = alpha, and y(1) = beta. A numeric al procedure is presented based on spline functions of degree five and six. Detailed error analysis and sixth order convergence of the schem e are discussed. Finally, computational efficiency and the convergence order are verified through numerical examples. For the sake of compar ison, results using some well-known methods are also tabulated.