Differential equations are fundamental tools in physics: they are used to describe phenomena ranging from fluid dynamics to general relativity. But when these equations become stiff (i.e. they involve ...

Researchers from the Institute of Cosmos Sciences of the University of Barcelona (ICCUB) have developed a new framework based ...

This unique book on ordinary differential equations addresses practical issues of composing and solving differential equations by demonstrating the detailed solutions of more than 1,000 examples. The ...

Abstract: This research intends to create a novel approach for solving fractional differential equations (FDEs) of both linear and nonlinear types utilizing the fractional shifted Legendre neural ...

ABSTRACT: This work focuses on the development and analysis of a financial system using advanced mathematical modeling techniques. Starting from an ordinary financial system, we extend it to a ...

To view the SciML Tutorials, go to tutorials.sciml.ai. By default, this will lead to the latest tagged version of the tutorials. To see the in-development version of the tutorials, go to ...

We study the existence of positive solutions of the equation u״ (t) + a (t) f (u(g(t))) = 0, 0 < t < 1 with linear boundary conditions. We show the existence of at least one positive solution if f is ...

To mathematicians, equations are art. Just as many are moved by a painting or piece of music, to those who appreciate and understand math, expressions of numbers, variables, operations and relations ...

Abstract: Based on deep neural network, elliptic partial differential equations in complex regions are solved. Accurate and effective strategies and numerical methods for elliptic partial differential ...