A class of singularly perturbed two point Boundary Value Problems (BVPs) of reaction-diffusion type for third order Ordinary Differential Equations (ODEs) with a small positive parameter (ε) multiplying the highest derivative and a discontinuous source term is considered. The BVP is reduced to a weakly coupled system consisting of one first order ordinary differential equation with a suitable i...

We will focus on the case where x can be solved for explicitly, i.e., the equation takes the form x = f(t, x, x, . . . , x), and where the function f mapping a subset of R×(F) into F is continuous. This equation is called an m-order n × n system of ODE’s. Note that if x is a solution defined on an interval I ⊂ R then the existence of x on I (including one-sided limits at the endpoints of I) imp...

Since their Newtonian inception, differential equations have been a fundamental tool for modeling the natural world. As the name suggests, these equations involve the derivatives of dependent variables (e.g. viral load, species densities, genotypic frequencies) with respect to independent variables (e.g. time, space). When the independent variable is scalar, the differential equation is called ...

subject to the constraint that q(0) and q(h) are constant. Standard ODE theory provides existence and uniqueness of the corresponding initial value problem because the derivatives q~(t) of the evolution curves q(t) are the integral curves of the corresponding Lagrangian vector field XE. Given two nearby ql, q2 6 Q, does there exist a unique evolution curve q(t) such that q(0) = q~ and q(h) = q2...

the numerical methods are of great importance for approximating the solutions of nonlinear ordinary or partial differential equations, especially when the nonlinear differential equation under consideration faces difficulties in obtaining its exact solution. in this latter case, we usually resort to one of the efficient numerical methods. in this paper, the chebyshev collocation method is sugge...

In this present study analytical method based on Riccati Equation as for converting the Nonlinear Lakshmanan-Porsezian-Daniel (LPD) equation into the nonlinear ODE and finding soliton solutions of this sustem discused. Obtaining solutions are new and obtained from wave transformation. The obtained results show that the presented method is effective and appropriate for solving nonlinear differen...

Sometimes an ordinary differential equation (ODE) solver gives the results it should, even if they are unexpected or undesirable. To obtain correct, expected numerical results, both relative and absolute error control tolerances must be chosen judiciously. Here we attempt to clear up some possible misunderstandings regarding the performance of a popular ODE solver and error control.

in this paper, differential transform method (dtm) is described and is applied to solve systems of nonlinear ordinary differential equations which is arising in hiv infections of cell. intervals of validity of the solution will be extended by using pade approximation. the results also will be compared with those results obtained by runge-kutta method. the technique is described and is illustrat...

Generalized Polya urn models can describe the dynamics of finite populations of interacting genotypes. Three basic questions these models can address are: Under what conditions does a population exhibit growth? On the event of growth, at what rate does the population increase? What is the long term behavior of the distribution of genotypes? To address these questions, we associate a mean limit ...

For time integration of transient eddy current problems commonly implicit time integration methods are used, where in every time step one or several nonlinear systems of equations have to be linearized with the Newton-Raphson method due to ferromagnetic materials involved. In this paper, a generalized Schur-complement is applied to the magnetic vector potential formulation, which converts a dif...