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 ...

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 ...

Abstract: This paper explores the reliability of the Chebyshev collocation Method (CCM) as a numerical approach used for solving a specific class of equations known as the second-order Fredholm ...

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 ...

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

ABSTRACT: The two-dimensional nonlinear shallow water equations in the presence of Coriolis force and bottom topography are solved numerically using the fractional steps method. The fractional steps ...