Differential-Difference Equations

equations relating an argument and an unknown function and the latter’s derivatives and increments (differences). For example, y’ = kΔy, where y = y(x) and Δy = y(x + h) - y(x). Substituting the last expression into the initial equation shows that the differential-difference equation is a special case of a differential equation with a diverging argument. Therefore, differential-difference equations are studied within the framework of this wider class of equations.

References in periodicals archive ?

Singular perturbation analysis of boundary-value problems for differential-difference equations. SIAM J.

A Numerical Scheme for Singularly Perturbed Delay Differential Equations of Convection-Diffusion Type on an Adaptive Grid

Aslan, "Traveling wave solutions for nonlinear differential-difference equations of rational types," Communications in Theoretical Physics, vol.

Exact Solutions with Variable Coefficient Function Forms for Conformable Fractional Partial Differential Equations by an Auxiliary Equation Method

Zheng, "Value distribution of meromorphic solutions of homogeneous and non-homogeneous complex linear differential-difference equations," Open Math, vol.

Some Properties of Solutions for Some q-Difference Equations Containing Painleve Equation

Bellman, Differential-Difference Equations, Academic Press, New York, NY, USA, 1963.

Numerical Study for Time Delay Multistrain Tuberculosis Model of Fractional Order

Decomposition of the Differential-Difference Equations

Algebro-Geometric Solutions for a Discrete Integrable Equation

Cui, "Improved reproducing kernel method for singularly perturbed differential-difference equations with boundary layer behavior," Applied Mathematics and Computation, vol.

An Asymptotic-Numerical Hybrid Method for Solving Singularly Perturbed Linear Delay Differential Equations

Stamov, Stability processes of moving invariant manifolds in uncertain impulsive differential-difference equations, Math.

On the Existence and Stability of Integral Manifolds for Fractional Functional Differential Systems

Singh, A Liapunov inequality and nonoscillation theorem for a second order nonlinear differential-difference equations, J.

Lyapunov type inequalities for second order sub and super-half-linear differential equations

Austin, An alternative approach to differential-difference Equations using the variational iteration method, Z.

ADOMIAN'S DECOMPOSITION METHOD FOR SOLVING FRACTIONAL GINZBURG-LANDAU EQUATION ARISING IN MATHEMATICAL PHYSICS USING JUMARIE'S FRACTIONAL DERIVATIVE

In this paper, we will discuss the interior layer for a class of nonlinear singularly perturbed differential-difference equations and construct its asymptotic expansion formula.

The asymptotic solutions for a class of nonlinear singular perturbed differential systems with time delays

Gu, "Discretized Lyapunov-Krasovskii functional for coupled differential-difference equations with multiple delay channels," Automatica, vol.

Stability analysis of Runge-Kutta methods for nonlinear functional differential and functional equations

Yuzbasi, "A numerical approximation based on the Bessel functions of first kind for solutions of Riccati type differential-difference equations," Computers & Mathematics with Applications, vol.

Numerical solution of nonlinear fractional Volterra integro-differential equations via bernoulli polynomials