Sideways heat equation and wavelets. (English) Zbl 0858.65099

The aim of this paper is to present a new approach for solving the sideways heat equation, which is a model of an ill-posed problem. After a short representation of the problem a regularization technique in the sense of Tikhonov is performed. The method consists in applying wave basis decomposition of measured data. The Meyer wavelets are applied to formulate the regularized solution which is convergent to the exact one when a data error tends to zero. The results suggest that wavelets may be useful for solving certain ill-posed problems.


65M30 Numerical methods for ill-posed problems for initial value and initial-boundary value problems involving PDEs
35K05 Heat equation
35R25 Ill-posed problems for PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
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