Approximate and Information Aspects of the Numerical Solution of Unstable Integral and Pseudodifferential Equations

We present a survey of the latest results obtained in the field of numerical solutions of unstable integral and pseudodifferential equations. New versions of fully discrete projection and collocation methods are constructed and justified. It is shown that these versions are characterized by the opti...

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Bibliographic Details
Published in:Ukrainian mathematical journal 2018-08, Vol.70 (3), p.495-512
Main Authors: Solodkyi, S. H., Semenova, E. V.
Format: Article
Language:English
Subjects:
Algebra
Analysis
Applications of Mathematics
Collocation methods
Geometry
Integrals
Mathematics
Mathematics and Statistics
Statistics
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Summary:We present a survey of the latest results obtained in the field of numerical solutions of unstable integral and pseudodifferential equations. New versions of fully discrete projection and collocation methods are constructed and justified. It is shown that these versions are characterized by the optimal accuracy and cost efficiency, as far as the use of the computational resources is concerned.
ISSN:0041-5995
1573-9376
DOI:10.1007/s11253-018-1512-1