A comparison study of meshfree techniques for solving the two-dimensional linear hyperbolic telegraph equation

In this paper, a comparison between two common techniques based on the radial basis function (RBFs), direct and indirect approaches and their localized forms is performed to numerical investigation of the two-dimensional linear second-order hyperbolic telegraph equation. Four meshfree methods based on the strong form equation, the nonsymmetric radial basis function collocation method or Kansa's method, the method of approximate particular solutions and the localized versions of these methods are formulated and the performances of these methods for solving governing problem are compared. A time stepping approach is employed for the first and second order time derivatives. The multiquadrics (MQ) and inverse multiquadrics (IMQ) functions are used as basis functions for interpolating either unknown function or Laplacian of the unknown function in the proposed techniques. Some numerical results are given to demonstrate the validity and efficiency of these methods. Through the presented results, it can be observed that local versions of the methods have superior stability and efficiency and the global methods are sensitive to the shape parameter and large amount of collocation points.