A new reproducing kernel method for linear nonlocal boundary value problems

In the previous works, the authors developed the reproducing kernel method (RKM) for nonlocal boundary value problems. A key of the method is the construction of the reproducing kernel (RK) satisfying the homogenous boundary conditions (BCs) of the considered problems. However, it is very difficult to obtain the RK of a reproducing kernel space satisfying nonlocal BCs or nonlinear BCs. Even if the RK is found, its representation is also very complicated compared with the RK without any BCs. In this paper, we will present a new RKM for linear nonlocal boundary value problems. The method can avoid reducing the inhomogeneous BCs to homogeneous BCs and constructing RK satisfying homogeneous nonlocal linear BCs. Numerical examples are provided to show the effectiveness of the new method.