Scientific Research Publishing

The Integral Equation, Corresponding to the Ordinary Differential Equation ()

The differential operator of the ordinary differential equation (ODE) is represented as the sum of two operators: basic and supplementing operators. The order of the higher derivatives of a basic ...
JSTOR Daily

On the Complete Integrability and Linearization of Nonlinear Ordinary Differential Equations. II. Third-Order Equations

We introduce a method for finding general solutions of third-order nonlinear differential equations by extending the modified Prelle-Singer method. We describe a procedure to deduce all the integrals ...
JSTOR Daily

On the Complete Integrability and Linearization of Nonlinear Ordinary Differential Equations. IV. Coupled Second-Order Equations

Coupled second-order nonlinear differential equations are of fundamental importance in dynamics. In this part of our study on the integrability and linearization of nonlinear ordinary differential ...
Scientific Research Publishing

Mixture of a New Integral Transform and Homotopy Perturbation Method for Solving Nonlinear Partial Differential Equations ()

Department of Mathematics, Polytechnic University of Tirana, Tirana, Albania. Department of Mathematics, University of Vlora, Vlora, Albania. A new integral transform is derived from the classical ...
Nature

Numerical Solution of Differential and Integral Equations

Numerical methods for differential and integral equations are indispensable in modern applied mathematics and engineering, offering tools to approximate complex physical phenomena where analytical ...
PNAS

Bridging the gap between models based on ordinary, delayed, and fractional differentials equations through integral kernels

This study centers on incorporating memory effects (the impact of past events on current states) into mathematical models for population dynamics. It introduces a framework based on the gamma ...
University of Waterloo

Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations

Implications of the choice of quadrature nodes for Picard integral deferred corrections methods for ordinary differential equations. BIT Numerical Mathematics, 45, 341–373.
GitHub

A Guide to Neural Ordinary Differential Equations

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 ...