Simplified Boundary Knot Method with Ghost Points for High-Order Harmonic-Type PDEs

In this paper, a new approach named simplified boundary knot method with ghost points (SBKM-G) is proposed to improve the performance of SBKM in solving high-order harmonic-type partial differential equations (PDEs). In contrast to the traditional SBKM where the source points are coincident with the collocation nodes on the boundary, the SBKM-G removes the source/ghost nodes to an arbitrary area like a circle (sphere) which covers the original problem domain in 2D (3D). This modification leads to higher accuracy without sacrificing simplicity and efficiency. In addition, the effect of free parameters in SBKM-G has also been studied. Numerical examples in 2D and 3D show the superiority of SBKM-G to SBKM and the performance of SBKM-G in solving this type of high-order PDEs is highlighted.