Numerical Solution of the Regularized Long Wave Equation using Radial Basis Function Ghost Point Method

The outcomes of numerical research of the 1-D Regularized Long Wave (RLW) equation using the meshless Radial Basis Function (RBF) collocation Ghost point Method are presented in this research paper. The RLW equation is frequently applied to solitons and to the study of water waves and other fluid mechanics problems. The paper suggests applying the RBF-Collocation method, which uses ghost points to set the boundary conditions, and uses it to analyze the RLW equation for different values of initial & boundary conditions and parameters. The proposed method is accurate and efficient because it matches the solutions found in the available literature for exactly solvable and analytical cases. The results indicate that the RBF-Collocation ghost point method is helpful for solving the RLW equation and can be applied to many real-world problems. The research paper contributes to developing numerical methods for solving partial differential equations without using meshes.