A Liapunov functional for a matrix difference-differential equation

A Liapunov Functional for a Linear Integral Equation

(2) C(t, s) ≥ 0, Cs(t, s) ≥ 0, Cst(t, s) ≤ 0, Ct(t, s) ≤ 0. The subscripts denote the usual partial derivatives and a is continuous. Convex kernels for both integral and integrodifferential equations are commonly used in the study of many real-world problems. Discussions may be found in Volterra [13], Grippenberg-Londen-Staffans [7; see index], Londen [10], and throughout Burton [4], for exampl...

Differential transformation method for solving a neutral functional-differential equation with proportional delays

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...

A period 5 difference equation

The main goal of this note is to introduce another second-order differenceequation where every nontrivial solution is of minimal period 5, namelythe difference equation:xn+1 =1 + xn−1xnxn−1 − 1, n = 1, 2, 3, . . .with initial conditions x0 and x1 any real numbers such that x0x1 6= 1.

Differential Equation of Sensitivity Matrix for Final Velocity Constraint

differential transformation method for solving a neutral functional-differential equation with proportional delays

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...