APPROXIMATE SOLUTIONS OF GENERAL NONLINEAR BOUNDARY-VALUE-PROBLEMS USING SUBDIVISION TECHNIQUES

A special class of basis functions generated by uniform subdivision al gorithms is used to formulate a high accuracy algorithm for the comput ation of approximate solutions of general two point boundary value pro blems of differential equations with or without deviating arguments. T his approach, which is different from the traditional finite differenc e or finite element method, produces non-polynomial/non-spline type, b ut continuous and differentiable approximate solutions to the boundary value problems provided the parameters of the algorithm are chosen ap propriately. The main ideas of the method are generation of basis func tions, node collocation, and boundary treatments. Numerical examples o f various types of non-linear two-point boundary value problems are in cluded to show the fast convergence and high accuracy of the algorithm . This paper is a further development of our previous work for solving linear boundary value problems and boundary value problems with devia ting arguments.