Differential equations arise in mathematics, physics, medicine, pharmacology, communications, image processing and animation, etc. An Ordinary Differential Equation (ODE) is a differential equation if it involves derivatives with respect to only one independent variable which can be studied from different perspectives; such as: analytical methods, graphical methods and numerical methods. This r...

By means of the Schechter’s Linking method, we study the existence of 2T -periodic solutions of the non-autonomous fourth-order ordinary differential equation u′′′′ −Au′′ −Bu− Vu(t, u) = 0 where A > 0, B > 0, V (t, u) ∈ C1(R × R,R) is 2T -periodic in t and satisfies either 0 < θV (t, u) ≤ uVu(t, u) with θ > 2, or uVu(t, u) − 2V (t, u) ≥ d3|u| with r ≥ 1.

In this paper an exponentially fitted finite difference method is presented for solving singularly perturbed two-point boundary value problems with the boundary layer. A fitting factor is introduced and the model equation is discretized by a finite difference scheme on an uniform mesh. Thomas algorithm is used to solve the tri-diagonal system. The stability of the algorithm is investigated. It ...

this paper presents the jeffery hamel flow of a non-newtonian fluid namely casson fluid. suitable similarity transform is applied to reduce governing nonlinear partial differential equations to a much simpler ordinary differential equation. variation of parameters method (vpm) is then employed to solve resulting equation. same problem is solved numerical by using runge-kutta order 4 method. a c...

Abstract The main goal of this paper is to developed a high-order and accurate method for the solution one-dimensional generalized Burgers-Fisher with Numman boundary conditions. We combined between fourth-order compact finite difference scheme spatial part diagonal implicit Runge Kutta in temporal part. In addition, we discretized points by using terms fourth order accuracy. This combine leads...

H = xy(2y − x− 2t)− 2β1y − β2x+ zw(2w − z − 2t)− 2β3w − β4z + 4yzw = HIV (x, y, t; β1, β2) +HIV (z, w, t; β3, β4) + 4yzw. Here, x, y, z and w denote unknown complex variables, and β1, β2, β3 and β4 are complex parameters. It is well-known that PIV has a confluence to the second Painlevé equation PII , where two accessible singularities come together into a single singularity. This suggests the ...