Operator Splitting and Global Error Analysis
Operator splitting is a widely used procedure in the mathematical modeling of physical and chemical processes, e.g., in the investigation of air pollution transport. This method allows us to lead the original, usually rather complicated model back to a sequence of sub-models having much simpler structrne. In certain cases this procedure can be performed without loss of accuracy. However, in most real models it causes the appearance of a new type of error, the so-called splitting error. Treating this error, which is coupled to the numerical errors arising from the application of numerical methods for the solution of the sub-problems, is a crucial problem. This task is especially complicated in the case of non-linear processes, such as certain chemical processes. In this paper we investigate the effect of the splitting error and the chosen numerical method on the accuracy of the solution. Both theoretical and numerical results are presented.
KeywordsSplitting Method Operator Splitting Split Scheme Time Integration Step Sequential Splitting
Unable to display preview. Download preview PDF.
- 1.Csomós, P., Faragó, I. and Havasi, Á. (2002) Weighted sequential splitting and its mathematical and numerical analysis,¡, submitted.Google Scholar
- 2.Dekker, K. and Verwer, J. G. (1984) Stability of Runge-Kutta methods for stiff non-linear differential equations, CWI Monographs 2, North-Holland Publishing Co., Amsterdam.Google Scholar
- 3.Dimov, I., Faragó, I., Havasi, Á and Zlatev, Z. (2002) L-commutativity of operators for splitting methods in air pollution models, Annal. Univ. Sci. Sec. Math. 44, pp. 127–148.Google Scholar
- 4.Havasi, A, Bartholy, J. and Faragó, I. (2001) Splitting method and its application in air pollution modeling, Idöjárás 105, pp. 39–58.Google Scholar
- 5.Marchuk, G. I. (1988) Methods of Splitting, Nauka. Moscow.Google Scholar
- 6.Stoer, J. and Bulirsch, R. (1993) Introduction to numerical analysis, Springer-Verlag.Google Scholar
- 8.Zlatev, Z., Computer Treatment of Large Air Pollution Models, Kluwer Academic Publishers.Google Scholar