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

• Main Author: Abdelmajid El Hajaji
• Format: Article
• Language: English
• Published: Sociedade Brasileira de Matemática 2017-10-01
• Series: Boletim da Sociedade Paranaense de Matemática
• Subjects: Convection-diffusion equation, theta-method, Spline collocation method.
• Online Access: http://periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/28664

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.