We find two factors of the product of the constant term (the term with no variable) and the coefficient of the squared variable whose sum gives the linear term. These factors are now placed in ...

Iterative methods form the backbone of numerical strategies for locating solutions of nonlinear equations, where direct analytic solutions are often unavailable. At their essence, these algorithms ...

In this paper, a new iterative formula for solving ordinary and partial nonlinear differential equations is derived based on the combination between Bernstein’s polynomial and the Adomian ...

This work introduces a model-agnostic framework for training and inference to enable accurate partial differential equation solving (down to double precision) for problems with arbitrary sizes and ...

Polynomial equations are a cornerstone of modern science, providing a mathematical basis for celestial mechanics, computer graphics, market growth predictions and much more. But although most high ...

Recent advancements in quantum computing and quantum-inspired algorithms have sparked renewed interest in binary optimization. These hardware and software innovations promise to revolutionize solution ...

ABSTRACT: This study compares the Adomian Decomposition Method (ADM) and the Variational Iteration Method (VIM) for solving nonlinear differential equations in engineering. Differential equations are ...

Abstract: This article proposes the MQHSS-Uzawa iterative method to solve the Navier-Stokes equation based on the MQHSS method and the Uzawa algorithm, and obtains and proves the convergence theorem ...