Scientific Research Publishing

C. H. Edwards and D. E. Penney, “Elementary Differential Equations,” 6th Edition, Pearson Prentice Hall, Upper Saddle River, 2008, pp. 340-345.

ABSTRACT: In this paper, we propose a unified differential operator method to study mechanical vibrations, solving inhomogeneous linear ordinary differential equations with constant coefficients. The ...
Europe PMC

Numerical solution of linear integro-differential equations by using generalized Bernstein operator collocation method

In this paper, we use the generalized Bernstein operator collocation method to compute weak singular kernel differential integral equations. We reconstruct the differential matrix form according to ...
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 ...
GitHub

Solving Ordinary Differential Equations Numerical Method Implementation in Python

Euler Method: The simplest numerical method for solving ODEs, which uses the derivative to project forward. [ y_{n+1} = y_n + h \cdot f(x_n, y_n) ] Heun's Method (Improved Euler Method): A two-step ...
Europe PMC

Learning Only on Boundaries: A Physics-Informed Neural Operator for Solving Parametric Partial Differential Equations in Complex Geometries.

Recently, deep learning surrogates and neural operators have shown promise in solving partial differential equations (PDEs). However, they often require a large amount of training data and are limited ...
marktechpost

Newton Informed Neural Operator: A Novel Machine Learning Approach for Computing Multiple Solutions of Nonlinear Partials Differential Equations

Neural networks have been widely used to solve partial differential equations (PDEs) in different fields, such as biology, physics, and materials science. Although current research focuses on PDEs ...
IEEE

Fast Solving Partial Differential Equations via Imitative Fourier Neural Operator

Abstract: Neural operators are a class of neural networks to learn mappings between infinite-dimensional function spaces, and recent studies have shown that using neural operators to solve partial ...