Numerical solution of non-conservative linear transport problems

Abstract

In this study, trigonometric cubic B-spline differential quadrature method is developed for a linear transport problems constructed on the advection-diffusion equation. The weighting coefficients used in the derivative approximations are determined by using the proposed algorithm. Following the space discretization of the advectiondiffusion equation, the resultant ODE system is integrated in time by using Rosenbrock implicit method of order four. The accuracy and validity of the proposed method are indicated by solving some initial boundary value problems (IBVPs) representing fade out of an initial positive pulse. The error between the analytical and the numerical solutions is measured by using the discrete maximum norm.