Local RBF-FD and LRBF-DQM Based Meshfree Algorithms for Computational Modeling of Wave Models

This article offered two meshfree algorithms namely local RBF-FD (LRBF-FD) approximation and local RBF-DQ method (LRBF-DQM) to simulate the 2nd order hyperbolic wave models (HVMs). In the evolvement of the first algorithm, time derivative is discretized by forward FD scheme and Crank-Nicolson scheme is used for rest of the terms. After that, LRBF-FD approximation is used for spatial discretization and quasi-linearization process for linearization the problem. Finally, the obtained linear system is solved by LU decomposition method. In the development of second algorithm, semi-discretization in space is done via LRBF-DQM and then an explicit RK4 is used for fully discretization in time. Stability analysis of the second algorithm has been discussed. For simulation purpose, some HVMs namely telegraph (TG), Klein-Gordon (KG), Sine-Gordon (SG), Vander Pol type (VPT) and Dissipative (DP) wave models are pondered to instigate the chastity and competence of the developed algorithms.