A ninth-order convergent method for solving the steady state reaction-diffusion model. (English) Zbl 1338.35247
Summary: The paper deals with a steady state version of a nonlocal nonlinear parabolic problem defined on a bounded polygonal domain. The nonlocal term involved in the strong formulation essentially increases the complexity of the problem and the necessary total computational work. The nonlinear weak formulation of the problem is reduced to a linear one suitable for applications of Newtonian type iterative methods. A discrete problem is obtained by the FEM. A fast and stable iterative method with ninth-order of convergence is applied for solving the discrete problem. The iterative algorithm is described by a pseudo-code. The method is computer implemented and the approximate solutions are presented graphically.
MSC:
| 35K57 | Reaction-diffusion equations |
| 65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
Keywords:
steady state reaction-diffusion model; inhomogeneous strong Allee effect; nonlocal problem; iterative methods; finite element approximationsReferences:
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