Sk. Bhatta et Ks. Sastri, A 6TH ORDER SPLINE PROCEDURE FOR A CLASS OF NONLINEAR BOUNDARY-VALUE-PROBLEMS, International journal of computer mathematics, 49(3-4), 1993, pp. 255-271
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.