No abstract

No abstract

In this paper, we present a numerical method for solving delay differential equations (DDEs). The method utilizes radial basis functions (RBFs). Error analysis is presented for this method. Finally, numerical examples are included to show the validity and efficiency of the new technique for solving DDEs.

We present a numerical method to solve boundary value problems (BVPs) for singularly perturbed differential-difference equations with negative shift. In recent papers, the term negative shift has been used for delay. The Bezier curves method can solve boundary value problems for singularly perturbed differential-difference equations. The approximation process is done in two steps. First we divide the time interval, intoksubintervals; second we approximate the trajectory and control functions in each subinterval by Bezier curves. We have chosen the Bezier curves as piecewise polynomials of degreenand determined Bezier curves on any subinterval byn+1control points. The proposed method is simple and computationally advantageous. Several numerical examples are solved using the presented method; we compared the computed result with exact solution and plotted the graphs of the solution of the problems.

In this paper, we describe a meshless approach to solve singularly perturbed differential-difference equations of the second order with boundary layer at one end of the interval. In the numerical treatment for such type of problems, first we approximate the terms containing negative and positive shifts which converts it to a singularly perturbed differential equation. Next, a numerical scheme based on the moving least squares (MLS) method is used for solving singularly perturbed differential equation. The MLS methodology is a meshless method, because it does not need any background mesh or cell structures. The proposed scheme is simple and efficient to approximate the unknown function. Several examples are presented to demonstrate the efficiency and validity of the numerical scheme presented in the paper.

No abstract

No abstract