Hossein Hosseinzadeh

In this thesis, the numerical solution of the two-dimensional hyperbolic telegraph equation is presented. For this purpose, radial basis functions based on finite differences are used for discretization of the space dimension, which, due to their high ability to approximate functions and high flexibility in modeling complex domains, provide the possibility of accurate and efficient solution of partial differential equations. Also, for discretization of the time dimension, the fourth-order Runge-Kutta method is used, which, due to its high accuracy and stability, increases the quality of numerical solution. The numerical results obtained from the implementation of this method indicate its acceptable accuracy and high efficiency in solving the two-dimensional hyperbolic telegraph equation. The obtained numerical results show that the proposed method can be used as an efficient and reliable tool for similar problems in the field of partial differential equations. In addition, the flexibility of the method in dealing with different boundary conditions and its ability to generalize to more complex problems are other important advantages of this method.