Google's second generation of its AI mathematics system combines a language model with a symbolic engine to solve complex geometry problems better than International Mathematical Olympiad (IMO) gold ...

This study introduced an efficient method for solving non-linear equations. Our approach enhances the traditional spectral conjugate gradient parameter, resulting in significant improvements in the ...

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 ...

Abstract: This study aimed at comparing the rate of convergence and performance of Newton-Raphson and Regula-Falsi method for solving the nonlinear equations. To solve nonlinear equations, two ...

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 ...

Presenting an algorithm that solves linear systems with sparse coefficient matrices asymptotically faster than matrix multiplication for any ω > 2. Our algorithm can be viewed as an efficient, ...

Secant method is an effective numerical technique for solving equations in mathematics. It’s a valuable tool for anyone looking to find approximate solutions to complex problems. In this article, we ...