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Numerical treatment of moving and free boundary value problems with the tau method. (English) Zbl 0999.65110
Summary: This paper reports numerical experiments on the implementation of the operational formulation of the tau method for moving and free boundary value problems. We consider problems defined by linear and nonlinear ordinary differential equations and by linear partial differential equations. We compare the accuracy attainable with the technique introduced in this paper with that of standard numerical techniques. We find that the tau method provides accurate results, even using approximations of a low degree.

MSC:
65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
35K15 Initial value problems for second-order parabolic equations
35R35 Free boundary problems for PDEs
80A22 Stefan problems, phase changes, etc.
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