A combined Method Of Lines and Orthogonal Collocation with Second kind Chebyshev nodes for convection–diffusion–reaction equation with Danckwerts Conditions

Abstract

We analyze and develop two numerical methods to solve the convection–diffusion–reaction equation with Danckwerts boundary conditions. One of the methods is an approach based on the method of lines using spatial discretization by orthogonal collocation. While this method has been applied to other equations, it has not been previously studied for this particular case. Furthermore, the convergence of the method is demonstrated for various values of the Péclet and Damköhler numbers. We also describe the implementation of a weighted residual method by orthogonal collocation method, using Lagrange polynomials and Chebyshev nodes of the second kind to solve the same problem. Both methods are presented in matrix form to facilitate its implementation in Matlab. Finally, we compare the results with both the analytical solution and those from a previous conventional method of lines discretization based on finite differences, implemented by the authors. The computed errors demonstrate that the adapted method of lines with orthogonal collocation yields a more accurate overall approximation than the alternative approaches.