A New Differential Quadrature Method Based on Bernstein Polynomials Firas Amer Al-Saadawi and Abdul-Sattar Jaber Ali Al-Saif

We propose a new technique of the differential quadrature method to find numerical solutions of the different transport (convection-diffusion) equations with appropriate initial and boundary conditions. The present method is based on the Bernstein polynomials formula, which is used to construct the weighting coefficients matrices of differential quadrature method, the new methodology is called Bernstein differential quadrature method (BDQM). Also, we improved alternating direction implicit formulation of differential quadrature method (ADI-DQM), based on Bernstein differential quadrature method (ADI-BDQM) for solving transport (convection-diffusion) equations. The results show that the differential quadrature technique renewed can be used as a powerful, reliable, accurate and efficient numerical tool in solving the transport problems. Finally, the many appearance of nonlinear differential equations as transport model in some fields of applied mathematics makes it necessary to... Это и многое другое вы найдете в книге A New Differential Quadrature Method Based on Bernstein Polynomials (Firas Amer Al-Saadawi and Abdul-Sattar Jaber Ali Al-Saif)