An adaptive pseudo-spectral method for reaction diffusion problems
An adaptive pseudo-spectral numerical method, solving systems of reaction, diffusion and convection equations is presented, which uses both Chebyshev and Galerkin approximations of the errors. The authors develop a family of functionals \(I_ r(u)\) with the property that the maximum norm of the error is bounded by \(I_ r(u)/J^ r\), where r is an integer and J is the degree of the polynomial approximation. These functionals are used in the adaptive procedure whereby the problem is dynamically transformed to minimize \(I_ r(u)\). The number of collocation points is then chosen to maintain a prescribed error bound. The method is llustrated by various examples from combustion problems in one and two dimensions. In the second section the authors describe the model and illustrate the features of the solution which make its numerical computation difficult. In section 3 the adaptive procedure is described and in the fourth section the functional which is used for the error estimation is given. In section 5 the authors illustrate the effectiveness of the proposed procedure by examples of the given model.
systems of reaction, diffusion and convection equations
scientific article; zbMATH DE number 4094737