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 ...

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 ...

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 ...

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 ...

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 ...

Department of Mathematical Sciences, Yeshiva University, New York, USA. Shandong Iron and Steel Company Ltd., Jinan, China. The State Key Laboratory of Tribology ...

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 ...