A polynomial based iterative method for linear parabolic equations
The following algorithm is proposed for linear parabolic equations on a bounded domain. A spatial discretization is introduced to get a method of lines, producing a system of ordinary differential equations, \(u_ t=- Lu+b.\) For a given time step \(\Delta\), an ellipse enclosing the spectrum of \(\Delta\) L is found, and on this ellipse the operator \((\Delta L)^{- 1}(e^{\Delta L}-1)\) is approximated by a finite expansion in terms of Chebychev polynomials. This expansion then serves to generate a pseudospectral method for the method of lines. The method is compared with an alternating-direction method and a locally one-dimensional method on a number of problems.
scientific article; zbMATH DE number 4124958
scientific article