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 [10] 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 (see e.g.

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