Name
Abstract | ||
|---|---|---|
Consider a system of ordinary differential equations (ODEs) dy/dt=f(t,y) where (a) t@?[a,b] with ba, (b) y is a vector containing s components and (c) y(a) is given. The @q-method is applied to solve approximately the system of ODEs on a set of prescribed grid points. If N is the number of time steps that are to be carried out, then this numerical method can be defined using the following set of relationships: y"n=y"n"-"1+h(1-@q)f(t"n"-"1,y"n"-"1)+h@qf(t"n,y"n),@q@?[0.5,1.0],n=1,2,...,N,h=(b-a)/N,t"n=t"n"-"1+h=t"0+nh,t"0=a,t"N=b. As a rule, the accuracy of approximations {y"n|n=1,2,...,N} can be improved by applying the Richardson Extrapolation under the assumption that the stability of the computational process is preserved. Therefore, it is natural to require that the combined numerical method (Richardson Extrapolation + the @q-method) is in some sense stable. It is proved in this paper that the combined method is strongly A-stable when @q@?[2/3,1.0]. It is furthermore shown that some theorems proved in a previous paper by the same authors, Farago et al. (2009) [1], are simple corollaries of the main result obtained in the present work. The usefulness of the main result in the solution of many problems arising in different scientific and engineering areas is demonstrated by performing a series of tests with an extremely badly scaled and very stiff atmospheric chemistry scheme which is actually used in several well-known large-scale air pollution models. |
Year | DOI | Venue |
|---|---|---|
2010 | 10.1016/j.cam.2010.05.052 | J. Computational Applied Mathematics |
Keywords | Field | DocType |
main result,numerical method,computational process,richardson extrapolation,prescribed grid point,combined method,combined numerical method,engineering area,previous paper,ordinary differential equation,stability,numerical methods,theorem proving,air pollution,atmospheric chemistry | Differential equation,Richardson extrapolation,Ordinary differential equation,Transcendental equation,Mathematical analysis,Algebraic equation,Extrapolation,Numerical analysis,Numerical stability,Mathematics | Journal |
Volume | Issue | ISSN |
235 | 2 | 0377-0427 |
Citations | PageRank | References |
5 | 0.78 | 1 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Zahari Zlatev | 1 | 205 | 65.20 |
| István Faragó | 2 | 62 | 21.50 |
| Ágnes Havasi | 3 | 39 | 9.98 |