An efficient differential quadrature method for fractional advection-diffusion equation
نویسندگان
چکیده
Abstract Using a set of modified cubic trigonometric B-splines as test functions, a new differential quadrature technique is proposed for the 1D and 2D transient advection-diffusion equations of order α ∈ (0, 1]. The weighted coefficients are determined via solving the system of algebraic equations with a strictly diagonally dominant tri-diagonal matrix. Then, the original equation is converted into an ordinary differential system (ODS), which is discretized by a third-order GorenfloMainardi-Moretti-Paradisi (GMMP) scheme in fractional case and by Runge-Kutta Gill’s method if α = 1. The resulting method is evaluated on four benchmark problems and a concrete simulation of the unsteady propagation of a Gaussian pulse. In comparison with the existent algorithms in open literature, the numerical results finally illustrate its validity and accuracy.
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