Solving nonlinear third-order three-point boundary value problems by boundary shape functions methods

Abstract For nonlinear third-order three-point boundary value problems (BVPs), we develop two algorithms to find solutions, which automatically satisfy the specified conditions. We construct a shape function (BSF), is designed conditions and can be employed new by assigning different roles of free in BSF. In first algorithm, let functions complete BSFs bases solution, not only automatically, but also used solution collocation technique. second BSF BVP another variable, such that transform corresponding initial problem for whose are given arbitrarily terminal values determined iterations; hence, quickly very accurate through few iterations. Numerical examples confirm performance algorithms.