Numerical solution to the telegraph equation via the geometric moving Kriging meshfree method

Abstract

Finding an appropriate shape function plays an important role in meshfree methods. Shape functions extracted from the moving Kriging (MK) interpolation is of recent interest for many researchers. We applied this technique to the weak form of the telegraph equation (TE) in space coordinates. Then we get a system of second-order ordinary differential equations w.r.t. the time variable. Some new variables are introduced to convert this system into a system of first-order ordinary differential equations. Then the resultant system is solved by the group preserving scheme (GPS). Examples are provided to demonstrate the power and accuracy of the proposed method for the one-dimensional hyperbolic TE.