Approximate solutions of general nonlinear boundary value problems using subdivision techniques

A special class of basis functions generated by uniform subdivision algorithms is used to formulate a high accuracy algorithm for the computation of approximate solutions of general two point boundary value problems of differential equations with or without deviating arguments. This approach, which is different from the traditional finite difference or finite element method, produces non-polynomial/non-spline type, but continuous and differentiable approximate solutions to the boundary value problems provided the parameters of the algorithm are chosen appropriately. The main ideas of the method are generation of basis functions, node collocation, and boundary treatments. Numerical examples of various types of non-linear two-point boundary value problems are included 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 deviating arguments.