A new algorithm for a class of linear nonlocal boundary value problems based on the reproducing kernel method

In this work, we present an algorithm for solving fourth-order multi-point boundary value problems (BVPs) based on the reproducing kernel method (RKM). In previous works, the RKM has been used to solve various two-point BVPs. However, it cannot be used directly to solve multi-point BVPs, since it is very difficult to obtain a reproducing kernel satisfying multi-point boundary conditions. The aim of this work is to fill this gap. A numerical example is given to demonstrate the efficiency of the present method. The results obtained show that the present method is quite reliable for linear fourth-order multi-point BVPs.