The stability problem of impulsive discrete systems with multiple delays is studied. By means of the Lyapunov stability theory and discrete-time Halanay-type inequality technique, we develop sufficient conditions for the exponential stability for the impulsive discrete systems with multiple delays, which involves multiple delays not only at non-impulsive time instants but also at impulsive time...

in this paper, we use a third degree b-spline function to construct an approximate solution forthird order linear and nonlinear boundary value problems coupled with the least square method. severalexamples are given to illustrate the efficiency of the proposed technique.

A family of fourth and second-order accurate numerical schemes is presented for the solution of nonlinear fourth-order boundary-value problems (BVPs) with two-point boundary conditions. Non-polynomial quintic spline functions are applied to construct the numerical algorithms. This approach generalizes nonpolynomial spline algorithms and provides a solution at every point of the range of integra...

The iterative computation of singular points in parametrized nonlinear BVPs by so-called extended systems requires good starting values for the singular point itself and the corresponding eigenfunction. Using path-following techniques such starting values for the singular points should be generated automatically. However, pathfollowing does not provide approximations for the eigenfunctions. We ...

In this paper, a singularly perturbed system of reaction–diffusion Boundary Value Problems (BVPs) is examined. To solve such a type of problems, a Modified Initial Value Technique (MIVT) is proposed on an appropriate piecewise uniform Shishkin mesh. The MIVT is shown to be of second order convergent (up to a logarithmic factor). Numerical results are presented which are in agreement with the th...

The study of multipoint BVPs for linear second-order ordinary differential equations was initiated by Il’in and Moiseev 1 . Since then many authors studied more general nonlinear multipoint boundary value problems. We refer readers to 2–5 and the references therein. Motivated by works mentioned above, in this paper, we study the existence of positive solutions for the following second-order sin...

Three parallel algorithms are presented for solving the Almost Block Diagonal (ABD) systems of linear algebraic equations that arise during the numerical solution of Boundary Value Problems (BVPs) for Ordinary Differential Equations (ODEs). Until recently, the solution of these systems has proven to be the execution-time bottleneck in the parallel implementation of most BVP codes. Several numer...

From Nagumo [10], there have been many accomplishments on the study of the existence of solutions for boundary value problems (BVPs) using the theory of differential inequality (cf. [1–9, 11–17]). However, for the nth-order nonlinear differential equations with the nonlinear boundary conditions, results are very few. The authors made some attempts to solve the nth-order Robin problem [14]. Now ...

Individual differences in impulsive and risky choice are key risk factors for a variety of maladaptive behaviors such as drug abuse, gambling, and obesity. In our rat model, ordered individual differences are stable across choice parameters, months of testing, and span a broad spectrum, suggesting that rats, like humans, exhibit trait-level impulsive and risky choice behaviors. In addition, imp...