Singular perturbations for systems of second order difference equations

NON-STANDARD FINITE DIFFERENCE METHOD FOR NUMERICAL SOLUTION OF SECOND ORDER LINEAR FREDHOLM INTEGRO-DIFFERENTIAL EQUATIONS

In this article we have considered a non-standard finite difference method for the solution of second order  Fredholm integro differential equation type initial value problems. The non-standard finite difference method and the composite trapezoidal quadrature method is used to transform the Fredholm integro-differential equation into a system of equations. We have also developed a numerical met...

Modified Laplace Decomposition Method for Singular IVPs in the second-Order Ordinary Differential Equations

  In this paper, we use modified Laplace decomposition method to solving initial value problems (IVP) of the second order ordinary differential equations. Theproposed method can be applied to linear and nonlinearproblems    

Research Article Unbounded Perturbations of Nonlinear Second-Order Difference Equations at Resonance

Singular Eigenvalue Problems for Second Order Linear Ordinary Differential Equations

We consider linear differential equations of the form (p(t)x′)′ + λq(t)x = 0 (p(t) > 0, q(t) > 0) (A) on an infinite interval [a,∞) and study the problem of finding those values of λ for which (A) has principal solutions x0(t;λ) vanishing at t = a. This problem may well be called a singular eigenvalue problem, since requiring x0(t;λ) to be a principal solution can be considered as a boundary co...

Numerical approximation for singular second order differential equations

We consider numerical approximation of solutions of singular second order differential equations. In particular, we study the backward (or implicit) Euler method. We prove results concerning consistency, global error and stability. We show that the global error is linear with respect to the step size. Numerical results are also given, which demonstrate the linear convergence and compare the num...