Fuzhang Wang^1,2, Enran Hou^2,*, Imtiaz Ahmad³, Hijaz Ahmad⁴, Yan Gu⁵

CMES-Computer Modeling in Engineering & Sciences, Vol.128, No.2, pp. 687-698, 2021, DOI:10.32604/cmes.2021.014739

Abstract Numerical solutions of the second-order one-dimensional hyperbolic telegraph equations are presented using the radial basis functions. The purpose of this paper is to propose a simple novel direct meshless scheme for solving hyperbolic telegraph equations. This is fulfilled by considering time variable as normal space variable. Under this scheme, there is no need to remove time-dependent variable during the whole solution process. Since the numerical solution accuracy depends on the condition of coefficient matrix derived from the radial basis function method. We propose a simple shifted domain method, which can avoid the full-coefficient interpolation matrix easily. Numerical experiments performed with… More >

Muhammad Amin¹, Muhammad Abbas^2,*, Dumitru Baleanu^3,4,5, Muhammad Kashif Iqbal⁶, Muhammad Bilal Riaz⁷

CMES-Computer Modeling in Engineering & Sciences, Vol.127, No.1, pp. 361-384, 2021, DOI:10.32604/cmes.2021.012720

Abstract This work is concerned with the application of a redefined set of extended uniform cubic B-spline (RECBS) functions for the numerical treatment of time-fractional Telegraph equation. The presented technique engages finite difference formulation for discretizing the Caputo time-fractional derivatives and RECBS functions to interpolate the solution curve along the spatial grid. Stability analysis of the scheme is provided to ensure that the errors do not amplify during the execution of the numerical procedure. The derivation of uniform convergence has also been presented. Some computational experiments are executed to verify the theoretical considerations. Numerical results are compared with the existing schemes… More >

C.Y. Lin¹, M.H. Gu¹, D.L. Young^1,2

CMC-Computers, Materials & Continua, Vol.18, No.1, pp. 43-68, 2010, DOI:10.3970/cmc.2010.018.043

Abstract The telegraph equations are solved by using the meshless numerical method called the time-marching method of fundamental solutions (TMMFS) in this paper. The present method is based on the method of fundamental solutions, the method of particular solutions and the Houbolt finite difference scheme. The TMMFS is a meshless numerical method, and has the advantages of no mesh building and numerical quadrature. Therefore in this study we eventually solved the multi-dimensional telegraph equation problems in irregular domain. There are totally six numerical examples demonstrated, in order they are one-dimensional telegraph equation, one-dimensional non-decaying telegraph problem, two-dimensional telegraph equation in irregular… More >