A localized transform-based meshless method for solving time fractional wave-diffusion equation

摘要

In the present work, a hybrid transform-based localized meshless method is constructed for the solution of fractional diffusion-wave equations. The time stepping procedure is avoided to overcome the problem of time in-stability related to meshless methods. The issue of ill conditioning related to meshless differentiation matrices is resolved by incorporating small local system matrices. The time fractional diffusion-wave equation is selected to test the method. A clear improvement is observed in terms of stability, accuracy and ill-conditioning.