A new fixed point theorem on cones is applied to obtain the existence of at least two positive solutions of a higher-order three-point boundary value problem for the differential equation subject to a class of boundary value conditions. The associated Green's function is given. Some results obtained recently are generalized. 1. Introduction. The multipoint boundary value problems for ordinary d...

We show deterministic polynomial time algorithms over some family of finite fields for solving univariate polynomial equations and some related problems such as taking nth roots, constructing nth nonresidues, constructing primitive elements and computing elliptic curve “nth roots”. In additional, we present a deterministic polynomial time primality test for some family of integers. All algorith...

A tiie-differencing scheme consisting of an initializing step and N repetitions of a set of steps is proposed. For linear equations, the scheme is of Nth order. It is easily programmed and uses a minimal amount of storage space. The order may be changed by changing one parameter. An improved scheme is of Nth order even for nonlinear equations , for N 54.

New integrability properties of a family sequences ordinary differential equations, which contains the Riccati and Abel chains as most simple sequences, are studied. The determination n generalized symmetries nth-order equation in each chain provides, without any kind integration, n-1 functionally independent first integrals equation. A remaining integral arises by quadrature using Jacobi last ...

in this article differential transformation method (dtms) has been used to solve neutral functional-differential equations with proportional delays. the method can simply be applied to many linear and nonlinear problems and is capable of reducing the size of computational work while still providing the series solution with fast convergence rate. exact solutions can also be obtained from the kno...

in this paper, we apply the differential transform (dt) method for finding approximate solution of the system of linear and nonlinear volterra integro-differential equations with variable coefficients, especially of higher order. we also obtain an error bound for the approximate solution. since, in this method the coefficients of taylor series expansion of solution is obtained by a recurrence r...