Journal:Applied Mathematics and Computation
Abstract:In this paper, we study a numerical algorithm to find all solutions of Gelfand equation. By utilizing finite difference discretization, the model problem defined on bounded do- main with Dirichlet condition is converted to a nonlinear algebraic system, which is solved by cascadic multigrid method combining with Newton iteration method. The key of our numerical method contains two parts: a good initial guess which is constructed via col- location technique, and the Newton iteration step is implemented in cascadic multigrid method. Numerical simulations for both one-dimensional and two-dimensional Gelfand equations are carried out which demonstrate the effectiveness of the proposed algorithm. We find that by using the symmetry property of equation, numerical solutions can be obtained by mirror reflection after solving model problem in a sub-domain. This will save considerable time consumption and storage cost in computational process of cascadic multigrid method.
First Author:Ruixue Sun
Indexed by:Journal paper
Correspondence Author:Y. Xu
Discipline:Natural Science
First-Level Discipline:Mathematics
Document Type:J
Volume:441
Page Number:1-12
Translation or Not:no
Included Journals:SCI