Because the presentation of this material in class will differ from that in the book, I felt that notes that closely follow the class presentation might be appreciated.

To integrate large systems of locally coupled ordinary differential equations (ODEs) with disparate timescales, we present a multirate method with error control that is based on the Cash-Karp Runge-Kutta (RK) formula. The order of multirate methods often depends on interpolating certain solution components with a polynomial of sufficiently high degree. By using cubic interpolants and analyzing ...

a new two-step implicit linear obrechkoff twelfth algebraic order method with vanished phase-lag and its first, second, third and fourth derivatives is constructed in this paper. the purpose of this paper is to develop an efficient algorithm for the approximate solution of the one-dimensional radial schrodinger equation and related problems. this algorithm belongs in the category of the multist...

in this paper, we introduce a hybrid approach based on neural network and optimization teqnique to solve ordinary differential equation. in proposed model we use heyperbolic secont transformation function in hiden layer of neural network part and bfgs teqnique in optimization part. in comparison with existing similar neural networks proposed model provides solutions with high accuracy. numerica...

Abstract. In this paper, a numerical solution for the system described by a generalized fractional Rikitake system is presented. The first step in the proposed procedure is represent the fractional order Rikitake system as an equivalent system of ordinary differential equations. In the second step, we solved the system obtained in the first step by using the well known fourth order Runge-Kutta ...