Characterization of non-disconjugacy for a one parameter family of nth-order linear differential equations

Computing the differential Galois group of a one-parameter family of second order linear differential equations

We develop algorithms to compute the differential Galois group corresponding to a one-parameter family of second order homogeneous ordinary linear differential equations with rational function coefficients. More precisely, we consider equations of the form ∂2Y ∂x2 + r1 ∂Y ∂x + r2Y = 0, where r1,r2 ∈C(x, t) and C is an algebraically closed field of characteristic zero. We work in the setting of ...

New family of Two-Parameters Iterative Methods for Non-Linear Equations with Fourth-Order Convergence

NON-STANDARD FINITE DIFFERENCE METHOD FOR NUMERICAL SOLUTION OF SECOND ORDER LINEAR FREDHOLM INTEGRO-DIFFERENTIAL EQUATIONS

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...

ON THE PERIODIC SOLUTIONS OF A CLASS OF nTH ORDER NONLINEAR DIFFERENTIAL EQUATIONS *

The nth order differential equation x + c (t )x + ƒ( t,x) = e(t),n>3 is considered. Using the Leray-Schauder principle, it is shown that under certain conditions on the functions involved, this equation possesses a periodic solution.

Disconjugacy of Second-order Linear Differential Equations with Non- Negative Coefficients

His basic criterion for disconjugacy turned out to be 1 0 is continuous and fal/P= °°, then the substitution t — fll/p transforms the first equation into one where p = l and the new f-interval is infinite. Thus this more general case reduces to Nehari's and again the criterion is 1 <X(o). However part of the whole picture seems to be lost by this transformation. If Ial...