In this paper, linear second-order differential equations of Sturm-Liouville type having a finite number of singularities and turning points in a finite interval are investigated. First, we obtain the dual equations associated with the Sturm-Liouville equation. Then, we prove the uniqueness theorem for the solutions of dual initial value problems.

in this article we have considered a non-standard finite difference method for the solution of second order  fredholm integro differential equation type initial value problems. the non-standard finite difference method and the composite trapezoidal quadrature method is used to transform the fredholm integro-differential equation into a system of equations. we have also developed a numerical met...

This paper presents a new symbolic algorithm to compute the singular initial value problem of second-order ordinary differential equations using Adomian decomposition method. The algorithm has been implemented in the computer algebra system Maple to facilitate the application of this method. A number of examples are presented to demonstrate the computation efficiency of the program. 2005 Elsevi...

Modified Adomian decomposition method has been used intensively to solve linear and nonlinear singular boundary and initial value problems. It has been proved to be very efficient in generating series solutions of the problem under consideration under the assumption that such series solution exits. The method is illustrated by some examples of higher order ordinary equations systems and series ...