A novel Chebyshev-collocation spectral method for solving the transport equation

Abstract

In this paper, we employ an efficient numerical method to solve transport equations with given boundary and initial conditions. By the weightedorthogonal Chebyshev polynomials, we design the corresponding basis functions for spatial variables, which guarantee the stiff matrix is sparse, for the spectral collocation methods. Combining with direct algebraic algorithms for the sparse discretized formula, we solve the equivalent scheme to get the numerical solutions with high accuracy. This collocation methods can be used to solve other kinds of models with limited computational costs, especially for the nonlinear partial differential equations. Some numerical results are listed to illustrate the high accuracy of this numerical method.