In this paper we discuss the numerical solution of initial-boundary value problem for the fourth order parabolic partial integro-differential equation. We use the forward Euler scheme for time discretization and the quasi-wavelet method for space discretization. Sometimes, we give a new method about the treatment of boundary condition. Numerical experiment is included to demonstrate the validit...

In this paper, we proposed a numerical integration method for the solution of singularly perturbed delay differential equation with dual layer behaviour. In this method, an asymptotically equivalent first order neutral type delay differential equation is obtained from the second order singularly perturbed delay differential equation and employed Trapezoidal rule on it. Then, linear interpolatio...

as x →∞, where x is the independent variable and the prime denotes d/dx. The functions pi(x) (0 ≤ i ≤ 2) and qi(x) (i = 1,2) are defined on an interval [a,∞), are not necessarily real-valued, and are all nowhere zero in this interval. Our aims are to identify relations between q0, q1, p0, p1, and p2 that represents an Euler case for (1.1) and to obtain the asymptotic forms of four linearly inde...

Oscillation and symmetry play an important role in many applications such as engineering, physics, medicine, vibration flight. The purpose of this article is to explore the oscillation fourth-order differential equations with delay arguments. New Kamenev-type oscillatory properties are established, which based on a suitable Riccati method reduce main equation into first-order inequality. Our ne...