Ordinary Differential Equations Notes for Mat 550 Spring 2013

Lecture Notes (spring 2012) 119b: Ordinary Differential Equations

APPLICATION NEURAL NETWORK TO SOLVE ORDINARY DIFFERENTIAL EQUATIONS

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...

Aims Lecture Notes 2006 10. Numerical Solution of Ordinary Differential Equations 10.1. First Order Systems of Ordinary Differential Equations. First Order Systems

This part is concerned with the numerical solution of initial value problems for systems of ordinary differential equations. We will introduce the most basic one-step methods, beginning with the most basic Euler scheme, and working up to the extremely popular Runge–Kutta fourth order method that can be successfully employed in most situations. We end with a brief discussion of stiff differentia...

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    

Numerical method for singularly perturbed fourth order ordinary differential equations of convection-diffusion type

In this paper, we have proposed a numerical method for singularly perturbed  fourth order ordinary differential equations of convection-diffusion type. The numerical method combines boundary value technique, asymptotic expansion approximation, shooting method and  finite difference method. In order to get a numerical solution for the derivative of the solution, the given interval is divided  in...