Solving Nonlinear Boundary Value Problems with Nonlinear Integral Boundary Conditions by Local and Nonlocal Boundary Shape Functions Methods

The paper considers the second-order nonlinear boundary value problem (NBVP), which is equipped with integral conditions (BCs). Two novel iterative algorithms are developed to overcome difficulty of NBVP double nonlinearities involved. In first algorithm, two nonlocal shape functions incorporating linear terms derived, and a function (NBSF) formulated assist solution. Let solution be NBSF so that can exactly transformed into an initial problem. new variable free in NBSF, its values given. For BCs, three unknown constants determined, while for five determined. Two-point local derived second wherein viewed as constants. By few iterations, four determined quickly. Through numerical experiments, these found powerful seeking quite accurate solutions. algorithm slightly better than first, fewer iterations more