This paper discusses a novel method of exact discretization obtaining an equivalent difference equation whose solution is equal to the solution of a differential equation at discrete periodic points.

This paper introduces a novel Galerkin algorithm, employing Bernoulli polynomials, to efficiently solve high-order differential equations and systems with homogeneous and nonhomogeneous initial ...

About This repository contains a Python implementation for solving ordinary differential equations (ODEs) using various numerical methods, including the Euler method, Heun's method, the Midpoint ...

In a remarkable step forward, a team of researchers has developed PROSE-PDE (Figure 3), a multimodal neural network model designed to be a foundation for solving a wide range of time-dependent PDEs, ...

In the past few years, fractional differential equations have emerged as a strong and well-organized mathematical tool in the study of many occurrences in science and engineering. Research in ...

Differential equations are equations that involve an unknown function and its derivatives with respect to one or more independent variables. They play a fundamental role in various fields of science, ...

The honor, like a Nobel Prize for mathematics, was given this year to Luis Caffarelli for his work on partial differential equations. By Kenneth Chang As a mathematician, Luis A. Caffarelli of the ...

We propose a new symmetry reduction method for (1+1)-dimensional differential-difference equations (DDEs), namely, the λ -symmetry reduction method of solving ordinary differential equations is ...