SYMMETRICAL SPLINE PROCEDURES FOR BOUNDARY-VALUE-PROBLEMS WITH MIXED BOUNDARY-CONDITIONS

Consider a class of boundary value problems of the form y'' = P(x)y + Q(x), a less-than-or-equal-to x less-than-or-equal-to b (linear) or y'' = f(x, y), a less-than-or-equal-to x less-than-or-equal-to b (nonlinear), subject to mixed boundary conditions y'(a)-Cy(a) = alpha, y'(b) + Dy(b) = beta. Symmetric global spline procedures are developed for the above-mentioned problems and their convergence is analysed. Finally computational efficiency and convergence orders are also illustrated through numerical examples.