以下では、E. Hairer、S. P. Nørsett、G. Wanner らによる名著シリーズ “Solving Ordinary Differential Equations”（日本語訳版: 『常微分方程式の数値解法』）について、詳しく解説します。 本シリーズは、非剛性（Nonstiff）から剛性（Stiff）、さらには微分代数方程式（DAE ...

Ordinary differential equations (ODEs) and difference equations serve as complementary tools in the mathematical modelling of processes evolving in continuous and discrete time respectively. Together ...

This repository contains an in-depth tutorial to help AI/ML practitioners successfully use neural ordinary differential equations (Neural ODEs or NODEs), understand the mathematics, know which types ...

MR MURRAY'S book is adapted to provide for students that knowledge of the subject of differential equations which they are likely to want in applications of mathematics to physics, and in the general ...

An intermediate level course in the analytical and numerical study of ordinary differential equations, with an emphasis on their applications to the real world. Exact solution methods for ordinary ...

SIAM Journal on Numerical Analysis, Vol. 27, No. 3 (Jun., 1990), pp. 704-735 (32 pages) Ordinary differential equations can be recast into a nonlinear canonical form called an S-system. Evidence for ...

Abstract: The data modeling of complex systems typically exhibits characteristics such as strong nonlinearity, variable redundancy, and abnormal data, all of which tend to decrease the model ...

We consider model selection and estimation in a context where there are competing ordinary differential equation (ODE) models, and all the models are special cases of a "full" model. We propose a ...

Abstract: Differential equations (DEs) serve as fundamental tools in mathematical modeling across scientific disciplines, yet classical numerical solvers face limitations with large-scale or ...