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A Tau method based on non-uniform space-time elements for the numerical simulation of solitons. (English) Zbl 0755.65124
This is an interesting paper where the Tau method is used for a nonlinear problem (Schrödinger’s cubic equation). The domain is subdivided into subdomains (space-time Tau elements) and the differential equation is considered separately in each subdomain with continuity conditions.
The nonlinear aspects are dealt with using iteration of linear problems and the Tau method is used for these problems so that the ‘right-hand side’ of the differential equation is a bivariate polynomial in $$x$$ and $$t$$ rather than zero.

##### MSC:
 65Z05 Applications to the sciences 65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs 35Q55 NLS equations (nonlinear Schrödinger equations) 81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
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