Implementation of a variable stepsize variable formula method in the time-integration part of a code for treatment of long-range transport of air pollutants. (English) Zbl 0558.65068
A system of two partial differential equations is used for modelling of long-range transport of pollutants over Europe. The first order space derivatives (the advection terms) are discretized by a pseudospectral algorithm. A discretization of the second order spatial derivatives (the diffusion terms) is carried out by a special technique developed. The arising large systems of ordinary differential equations are integrated by a variable stepsize variable formula method, which is based on the predictor-corrector scheme. The stepsize selection strategy and the formula selection strategy are explained in detail. An accuracy control and a stability control are performed for each time step. Numerical experiments with real meteorological data prove the great efficiency of the applied method and the reliability of the obtained results.
Reviewer: I.Dvořák
MSC:
| 65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |
| 65M50 | Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs |
| 35K25 | Higher-order parabolic equations |
| 92D40 | Ecology |
Keywords:
long-range transport of sulphur di-oxide and sulphate over Europe; advection; pseudospectral; diffusion; variable stepsize variable formula method; predictor-corrector schemes; stepsize selection strategy; formula selection strategy; accuracy control; stability control; numerical experiments; nitrogen pollutantsReferences:
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