This course provides an introduction to topics involving ordinary differential equations. Emphasis is placed on the development of abstract concepts and applications for first-order and linear ...

In this article, third- and fourth-order accurate explicit time integration methods are developed for effective analyses of various linear and nonlinear dynamic problems stated by second-order ...

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ABSTRACT: This study compares the Adomian Decomposition Method (ADM) and the Variational Iteration Method (VIM) for solving nonlinear differential equations in engineering. Differential equations are ...

ABSTRACT: To solve the first-order differential equation derived from the problem of a free-falling object and the problem arising from Newton’s law of cooling, the study compares the numerical ...

This paper addresses the limitations of current neural ordinary differential equations (NODEs) in modeling and predicting complex dynamics by introducing a novel framework called ...

This paper presents In-Context Operator Networks (ICON), a neural network approach that can learn new operators from prompted data during the inference stage without requiring any weight updates.