Application of Weighted Residual and Orthogonal Finite Element Computational Techniques to Nonlinear Boundary Value Problems
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Date
2021-05-25
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Addis Ababa University
Abstract
The main focus of this thesis is to examine the applications of weighted residual and orthogonal collocation finite element computational techniques to nonlinear boundary value problems. The application of WRM and OCFE method for solving nonlinear boundary value problems are examined. A detailed comparison with their procedures is made. The orthogonal collocation finite element method is compared to the Subdomain, Galerkin, and Collocation weighted residual methods and the advantage are illustrated. The sensitivity of the orthogonal collocation method to different parameters is studied. Orthogonal collocation on finite elements is used to solve nonlinear BVPs and its superiority over the weighted residual method is shown. To this end, application of Subdomain Weighted Residual method, Galerkin Weighted Residual method , Collocation Weighted Residual and the orthogonal collocation on finite elements is also used to solve nonlinear boundary value problems, namely the steady state exothermic chemical reaction in a slab of combustible material, the catalytic reactions in a flat particle, the thermal explosion in a vessel, Troesch boundary value problem for temperature distribution, reaction-diffusion equation and temperature distribution in straight fins with temperature dependent thermal conductivity to their respect mixed boundary conditions for different parameters. We also analyzed computational cost by measuring elapsed and CPU time for the applications of WRM and OCFEM. The results agree remarkably with those from the literature
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Keywords
Bvps, Weighted Residual, Subdomain Wrm, Galerkin Wrm, Collocation Wrm, Orthogonal Collocation Finite Element Method