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 ...

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 ...

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 ...

Abstract: Stability of the zero solution is studied for a linear integro-differential equation with operator coefficients. The coefficients are assumed to be linear, selfadjoint, commuting operators ...

Researchers have made a breakthrough in the ability to solve engineering problems. In a new paper published in Nature entitled, “A scalable framework for learning the geometry-dependent solution ...

ABSTRACT: The Modified Adomian Decomposition Method (MADM) is presented. A number of problems are solved to show the efficiency of the method. Further, a new solution scheme for solving boundary value ...

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

The data and code for the paper Neural-operator element method: Efficient and scalable finite element method enabled by reusable neural operators. This repository contains reference implementations ...