Wavelets and numerical pseudodifferential operator. (English) Zbl 1446.65029
Summary: Calculating the value for the pseudodifferential operator with unbounded symbol is an ill-posed problem. In the present paper we adopt a wavelet regularization method to solve this problem, error estimates of Hölder type between the regularized values and the exact values are derived. Applications of the general theory scheme and numerical test to the concrete problems are presented.
MSC:
| 65J20 | Numerical solutions of ill-posed problems in abstract spaces; regularization |
| 65T60 | Numerical methods for wavelets |
| 35R25 | Ill-posed problems for PDEs |
| 35S05 | Pseudodifferential operators as generalizations of partial differential operators |
Keywords:
numerical pseudodifferential operator; ill-posed problem; Meyer wavelet regularization; error estimate; numerical experimentsReferences:
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