Journals Information
Mathematics and Statistics Vol. 4(1), pp. 27 - 39
DOI: 10.13189/ms.2016.040104
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Asymptotic Solving Essentially Nonlinear Problems
Alexander D. Bruno *
Department of Singular Problem, Keldysh Institute of Applied Mathematics of RAS, Miusskaya sq. 4, 125047, Moscow, Russia
ABSTRACT
Here we present a way of computation of asymptotic expansions of solutions to algebraic and differential equations and present a survey of some of its applications. The way is based on ideas and algorithms of Power Geometry. Power Geometry has applications in Algebraic Geometry, Differential Algebra, Nonstandard Analysis, Microlocal Analysis, Group Analysis, Tropical/Idempotent Mathematics and so on. We also discuss a connection of Power Geometry with Idempotent Mathematics.
KEYWORDS
Singularity, Newton Polyhedron, Painleve Equation, Boundary Layer, Idempotent Analysis
Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Alexander D. Bruno , "Asymptotic Solving Essentially Nonlinear Problems," Mathematics and Statistics, Vol. 4, No. 1, pp. 27 - 39, 2016. DOI: 10.13189/ms.2016.040104.
(b). APA Format:
Alexander D. Bruno (2016). Asymptotic Solving Essentially Nonlinear Problems. Mathematics and Statistics, 4(1), 27 - 39. DOI: 10.13189/ms.2016.040104.