The aim of this paper is to obtain numerical solutions of the one-dimensional,two-dimensional and coupled Burgers' equations through the generalized differential quadrature method(GDQM).The polynomial-based differ...The aim of this paper is to obtain numerical solutions of the one-dimensional,two-dimensional and coupled Burgers' equations through the generalized differential quadrature method(GDQM).The polynomial-based differential quadrature(PDQ) method is employed and the obtained system of ordinary differential equations is solved via the total variation diminishing Runge-Kutta(TVD-RK) method.The numerical solutions are satisfactorily coincident with the exact solutions.The method can compete against the methods applied in the literature.展开更多
This paper present an implementation of＂modified cubic B-spline differential quadrature method （MCB-DQM）＂ proposed by Arora ＆ Singh （Applied Mathematics and Computation Vol. 224（1） （2013） 161-177） for numer...This paper present an implementation of＂modified cubic B-spline differential quadrature method （MCB-DQM）＂ proposed by Arora ＆ Singh （Applied Mathematics and Computation Vol. 224（1） （2013） 161-177） for numerical computation of Fokker-Planck equations. The modified cubic B-splines are used as set of basis functions in the differential quadrature to compute the weighting coefficients for the spatial derivatives, which reduces Fokker-Planck equation into system of first-order ordinary differential equations （ODEs）, in time. The well known SSP-RK43 scheme is then applied to solve the resulting system of ODEs. The efficiency of proposed method has been confirmed by three examples having their exact solutions. This shows that MCB-DQM results are capable of achieving high accuracy. Advantage of the scheme is that it can be applied very smoothly to solve the linear or nonlinear physical problems, and a very less storage space is required which causes less accumulation of numerical errors.展开更多
文摘The aim of this paper is to obtain numerical solutions of the one-dimensional,two-dimensional and coupled Burgers' equations through the generalized differential quadrature method(GDQM).The polynomial-based differential quadrature(PDQ) method is employed and the obtained system of ordinary differential equations is solved via the total variation diminishing Runge-Kutta(TVD-RK) method.The numerical solutions are satisfactorily coincident with the exact solutions.The method can compete against the methods applied in the literature.
文摘This paper present an implementation of＂modified cubic B-spline differential quadrature method （MCB-DQM）＂ proposed by Arora ＆ Singh （Applied Mathematics and Computation Vol. 224（1） （2013） 161-177） for numerical computation of Fokker-Planck equations. The modified cubic B-splines are used as set of basis functions in the differential quadrature to compute the weighting coefficients for the spatial derivatives, which reduces Fokker-Planck equation into system of first-order ordinary differential equations （ODEs）, in time. The well known SSP-RK43 scheme is then applied to solve the resulting system of ODEs. The efficiency of proposed method has been confirmed by three examples having their exact solutions. This shows that MCB-DQM results are capable of achieving high accuracy. Advantage of the scheme is that it can be applied very smoothly to solve the linear or nonlinear physical problems, and a very less storage space is required which causes less accumulation of numerical errors.
