In this paper, the localized method of fundamental solutions (LMFS) with coupling the dual reciprocity method (DRM) is applied to simulate three-space dimensional nonlinear wave equations. First, DRM, which is a popular meshless method based on polyharmonic splines (PhS), is applied to obtain the particular solution. After evaluating the particular solution, 3D-LMFS method can be employed to evaluate the homogeneous solution. The proposed 3D-LMFS algorithms construct 3D artificial surfaces where source points and then the collocation procedure propose by using the fundamental solutions in each...
