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Analysis of operator splitting for advection-diffusion-reaction problems from air pollution modelling. (English) Zbl 0949.65090
Operator or time splitting methods for the numerical solution of initial-boundary value problems for differential equations are discussed. Such a method is a standard practice for example in computational air pollution modelling. For such an approach it is important to estimate the quality of splitting and to determine the splitting error.
The paper presents an analysis of operator splitting aimed at providing insight into the splitting error. Using the Lie operator formalism a general expression is derived for the three-term Strang splitting in the pure initial value case. For the class of advection-diffusion reaction problems the splitting error is analyzed in detail.
A special case is discussed in which the splitting error can be reduced. Some results for an operator splitting in initial-boundary value problems are also developed.

MSC:
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65Y05 Parallel numerical computation
65Y20 Complexity and performance of numerical algorithms
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
65M20 Method of lines for initial value and initial-boundary value problems involving PDEs
35K57 Reaction-diffusion equations
92D40 Ecology
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