Boletim da Sociedade Paranaense de Matemática (Oct 2017)
A numerical method for solving time-dependent convection-diffusion problems
Abstract
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.
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