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


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.

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.