Numerical Treatment of IVP ODEs. . . in a Nutshell

Numerical Analysis of Ordinary Differential Equations

Since many ordinary differential equations (ODEs) do not have a closed solution, approximating them is an important problem in numerical analysis. This work formalizes a method to approximate solutions of ODEs in Isabelle/HOL. We formalize initial value problems (IVPs) of ODEs and prove the existence of a unique solution, i.e. the Picard-Lindelöf theorem. We introduce general one-step methods f...

Validated Numerical Bounds on the Global Error for Initial Value Problems for Stiff Ordinary Differential Equations

Validated Numerical Bounds on the Global Error for Initial Value Problems for Stiff Ordinary Differential Equations Chao Yu Master of Science Graduate Department of Computer Science University of Toronto 2004 There are many standard numerical methods for initial value problems (IVPs) for ordinary differential equations (ODEs). Compared with these methods, validated methods for IVPs for ODEs pro...

An efficient method for the numerical solution of Helmholtz type general two point boundary value problems in ODEs

In this article, we propose and analyze a computational method for numerical solution of general two point boundary value problems. Method is tested on problems to ensure the computational eciency. We have compared numerical results with results obtained by other method in literature. We conclude that propose method is computationally ecient and eective.

Numerical Solution of Hybrid Fuzzy Dierential Equation (IVP) by Improved Predictor-Corrector Method

RKSUITE 90: Software for ODE IVPs

We announce publicly available Fortran 90 software for the initial value problem (IVP) in ordinary diierential equations (ODEs). We describe the interfaces and how Fortran 90 language features aaord the opportunity both to address diierent types and structures of variables and to provide functionality not usually directly associated with IVP solvers.