Stability Restrictions on TimeStepsize for Numerical Integration of FirstOrder Partial Differential Equations
Abstract
Mathematical models described by partial differential equations appear often when different phenomena related to atmospheric transport (for example, advection and diffusion processes) are studied. Truncated Fourier series can be used in the discretization of the space derivatives resulting in a pseudospectral method. In this way the partial differential equation is transformed into a system of ordinary differential equations. This system is normally solved by socalled "stepbystep" integration methods. The stability properties of these methods are studied. Some bounds for the timestepsize are derived. Several formulae and predictorcorrector schemes with large stability intervals on the imaginary axis are constructed. Numerical experiments with eight timeintegration algorithms are carried out. Some recommendations concerning the choice of the timeintegration algorithms in three different situations are given. It is emphasized that in a package for the solution of partial differential equations describing transport processes in the atmospheric environment one should have several timeintegration algorithms, each of which can be chosen optionally. Finally, the possibility of using variable stepsize, variable formula timeintegration algorithms is briefly discussed.
 Publication:

Journal of Computational Physics
 Pub Date:
 July 1983
 DOI:
 10.1016/00219991(83)900797
 Bibcode:
 1983JCoPh..51....1Z