Our aim is for Cauchy problem (2.2), (2.1) for a linear singularly perturbed ordinary differential equation
, to study applicability of standard difference schemes for solving such problems; to construct and investigate a special difference scheme convergent [epsilon]-uniformly in the maximum norm, i.e., robust difference scheme.
The singular second-order ordinary differential equation
with periodic and deviated multipoint boundary conditions (1)-(2) is equivalent to the functional integral equation:
In the series of articles [8,11-14] the linearization problem of a third-order ordinary differential equation
via the contact transformations was solved.
Moreover, our aim is to relate geodesic curves of the metric connection to solution curves of given ordinary differential equation
simply as [mathematical expression not reproducible].
Omar, "Direct solution of second-order ordinary differential equation
using a single-step hybrid block method of order five," Mathematical and Computational Applications, vol.
On the other hand, for the ordinary differential equation
(with time delay), Takeuchi and Ma  have shown the global asymptotic stability of the solution (S(t), I(t), R(t)) of
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.
(2011) that with the physical parameters the system of partial differential equations could be replaced by a system of ordinary differential equations
because both systems gave identical results.
Using Proposition 3.1, we have the following correspondence between the eigenvalue problem and existence problem of holomorphic solutions of Heun's ordinary differential equation
Elzaki, On the Elzaki Transform and Ordinary Differential Equation
With Variable Coefficients, Advances in Theoretical and Applied Mathematics, ISSN 0973-4554 Volume 6, Number 1(2011), pp.
The second order linear ordinary differential equation
has the general form