Rational interpolation method for solving initial value problems (IVPs) in ordinary differential equations

An Implicit Rational Method for Solution of Second Order Initial Value Problems in Ordinary Differential Equations

In this article, we report an implicit rational method for solution of second order initial value problems in ordinary differential equation. We have presented local truncation error and stability property for the proposed method. We observed that the method has cubic rate of convergenceandA-stable. Numerical results for linear and nonlinear problems presented. These results confirm the accurac...

A quasi-interpolation method for solving stiff ordinary differential equations

Initial value problems for second order hybrid fuzzy differential equations

Usage of fuzzy differential equations (FDEs) is a natural way to model dynamical systems under possibilistic uncertainty. We consider second order hybrid fuzzy differentia

Validated solutions of initial value problems for ordinary differential equations

Compared to standard numerical methods for initial value problems (IVPs) for ordinary diierential equations (ODEs), validated methods for IVPs for ODEs have two important advantages: if they return a solution to a problem, then (1) the problem is guaranteed to have a unique solution, and (2) an enclosure of the true solution is produced. The authors survey Taylor series methods for validated so...

22 Initial Value Problems for Ordinary Differential Equations

We may be interested in the solution u(t) in a finite interval [t0, T ] or in the semi-infinite interval t ≥ t0. In most of this lecture f and u are real-valued functions. A generalization to vector-valued functions is important in applications and will be discussed at the end of the lecture. Numerical methods for the solution of the initial value problem (1)-(2) generate a sequence of values o...