Name
Title | ||
|---|---|---|
An ADI extrapolated Crank-Nicolson orthogonal spline collocation method for nonlinear reaction-diffusion systems |
Abstract | ||
|---|---|---|
An alternating direction implicit (ADI) orthogonal spline collocation (OSC) method is described for the approximate solution of a class of nonlinear reaction-diffusion systems. Its efficacy is demonstrated on the solution of well-known examples of such systems, specifically the Brusselator, Gray-Scott, Gierer-Meinhardt and Schnakenberg models, and comparisons are made with other numerical techniques considered in the literature. The new ADI method is based on an extrapolated Crank-Nicolson OSC method and is algebraically linear. It is efficient, requiring at each time level only O(N) operations where N is the number of unknowns. Moreover, it is shown to produce approximations which are of optimal global accuracy in various norms, and to possess superconvergence properties. |
Year | DOI | Venue |
|---|---|---|
2012 | 10.1016/j.jcp.2012.04.001 | J. Comput. Physics |
Keywords | Field | DocType |
nonlinear reaction-diffusion system,time level,approximate solution,numerical technique,new adi method,superconvergence property,schnakenberg model,crank-nicolson osc method,orthogonal spline collocation,optimal global accuracy,brusselator,alternating direction implicit method | Alternating direction implicit method,Mathematical optimization,Nonlinear system,Mathematical analysis,Spline collocation,Superconvergence,Reaction–diffusion system,Approximate solution,Mathematics,Crank–Nicolson method,Brusselator | Journal |
Volume | Issue | ISSN |
231 | 19 | 0021-9991 |
Citations | PageRank | References |
7 | 0.64 | 15 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Ryan I. Fernandes | 1 | 34 | 5.16 |
| Graeme Fairweather | 2 | 165 | 40.42 |