Dimova S.N.
Adaptive numerical procedures based on the invariant properties of the continuous models
ADAPTIVE NUMERICAL PROCEDURES BASED ON THE INVARIANT PROPERTIES
OF THE CONTINUOUS MODELS
S.N. Dimova
Faculty of Mathematics and Informatics
Sofia University “St. KL. Ohridski”, Sofia, Bulgaria
dimova@fmi.uni-sofia.bg
The successful constructing of discrete methods is based on the use of the known qualitative information about the continuous models and their solutions - symmetries, invariant properties, asymptotics. This idea is the basis of the geometric integration (see the monograph [1], the review paper [2] and the references therein), as well as of some moving mesh methods [3]. Adaptive numerical procedures, based on the known invariant properties of the differential problems and on the known regularity and asymptotic behavior of their solutions are presented in this lecture. They are illustrated by examples of quasilinear and semilinear reaction-diffusion problems.
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This work is partially supported by the National Science Fund of BMSE under grant I02/9/2014 and by the Science Fund of Sofia University under grant 75/2015.
REFERENCES
1. Hairer E., Lubich C., Wanner G. Geometric Numerical Integration. Structure-preserving Algorithms for ODE. Springer Verlag, 2002.
2. Budd C.J., Piggott M.D. Geometric integration and its applications, 2001. http://www.bath.ac.uk/~mascjb/home.html
3. Budd S.J., Huang W., Russel R.D. Moving mesh methods for problems with blow-up. // SIAM J. SCi. Comp., 1996. V. 17, iss. 2. P. 305-327.
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