It addresses dynamical systems governed by ordinary differential equations
, with applications of the theory of dynamical systems to physics, biology, chemistry, and engineering shown through examples.
At present, for wide classes of singularly perturbed boundary value problems with elliptic and ordinary differential equations
, and for initial boundary value problems with parabolic equations, special numerical methods based on standard difference schemes on grids condensing in boundary layers have been developed and well studied whose solutions converge [epsilon]-uniformly in the maximum norm (see, e.g., [1,2,6,10,11] and the bibliography therein).
From a review of ordinary differential equations
to complex analysis and principles of electromagnetism, quantum mechanics, and special relativity, this math-based concept guide may be used as either a classroom text or for individual study, and includes a disc of companion files and worksheets supporting the book's contents.
The singular ordinary differential equations
emerge in the fields of the theory of boundary layer, Newtonian fluid mechanics, gas dynamics, and so on.
Although linear ordinary differential equations
can be solved by a large number of methods but this situation does not hold for nonlinear equations.
Wilkens, "Linearization of second order ordinary differential equations
via Cartan's equivalence method," Journal of Differential Equations, vol.
It is worth mentioning that, in the last century, theory of ordinary differential equations
, functional differential equations, partially differential equations, integral equations, and integrodifferential equations has developed quickly and played many important roles in qualitative theory and applications of that equations.
Reference  established a new iteration improvement of the solution based on the dynamic system of ordinary differential equations
(ODEs), and the new method is more effective than Wilkinson's method.
An important class of linear ordinary differential equations
(LODEs) consists of those equations having a symmetry algebra of maximal dimension.
As there are complete comments and references of this result for ordinary differential equations
Pirbavafa, A generalization of Geraghty's theorem in partially ordered metric spaces and applications to ordinary differential equations
, Fixed Point Theory Appl., 74 (2012), 9 pages.