A numerical method for solving time-dependent convection-diffusion problems

Boletim da Sociedade Paranaense de Matemática

关键词: Convection-diffusion equation, theta-method, Spline collocation method.;   

DOI  :  10.5269/bspm.v35i1.28664

来源: DOAJ

【 摘 要 】

In this paper, we develop a new numerical method for solving a timedependent convection-diffusion equation with Dirichlet’s type boundary conditions. We first propose the theta-method to discretize the temporal variable, resulting in a linear partial differential equation (PDE). To numerically solve this linear PDE, we develop and we analyze a new cubic spline collocation method for the spatial discretization. To solve the discretized linear system, we design a collocation method and we prove that the method is second order convergent. The computed results are compared wherever possible with those already available in the literature.

【 授权许可】

Unknown