Numerical Treatment of Moving and Free Boundary Value Problems with the Tau Method

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 equa- tions. 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. This paper reports numerical experiments on the implementation of the operational formulation of the Tan Method for the numerical treatment of moving and free boundary value problems. We consider first problems involving linear and nonlinear ordinary differential equations and develop on them basic strategies for their Tau Method approximate solution. We then discuss a Tau-Lines formulation of these techniques and apply it to the approximate solution of a moving boundary value problem for partial differential equations. The problem considered is related to a model for the diffusion and absorption of oxygen in biological tissue. We compare our results with those obtained in the related literature using seven different numerical techniques. We find that the Tan Method provides accurate results, even using low degree polynomial approximations.

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