34,001 research outputs found
Perturbative Linearization of Reaction-Diffusion Equations
We develop perturbative expansions to obtain solutions for the initial-value
problems of two important reaction-diffusion systems, viz., the Fisher equation
and the time-dependent Ginzburg-Landau (TDGL) equation. The starting point of
our expansion is the corresponding singular-perturbation solution. This
approach transforms the solution of nonlinear reaction-diffusion equations into
the solution of a hierarchy of linear equations. Our numerical results
demonstrate that this hierarchy rapidly converges to the exact solution.Comment: 13 pages, 4 figures, latex2
Perturbative Linearization of Reaction-Diffusion Equations
Abstract We develop perturbative expansions to obtain solutions for the initial-value problems of two important reaction-diffusion systems, viz., the Fisher equation and the time-dependent Ginzburg-Landau (TDGL) equation. The starting point of our expansion is the corresponding singular-perturbation solution. This approach transforms the solution of nonlinear reaction-diffusion equations into the solution of a hierarchy of linear equations. Our numerical results demonstrate that this hierarchy rapidly converges to the exact solution
Numerical Methods for Singular Perturbation Problems
Consider the two-point boundary value problem for a stiff system of ordinary differential equations. An adaptive method to solve these problems even when turning points are present is discussed
- …