1 Institute of Data Science and Engineering, Xuzhou University of Technology, Xuzhou, China 2 School of Mathematics and Statistics, Huaibei Normal University, Huaibei, China This study introduces a ...

A UNSW Sydney mathematician has discovered a new method to tackle algebra's oldest challenge—solving higher polynomial equations. Polynomials are equations involving a variable raised to powers, such ...

First, we install the PyTorch and matplotlib libraries using pip, ensuring you have the necessary tools for building neural networks and visualizing the results in your Google Colab environment. Copy ...

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 ...

Abstract: Deep learning and machine learning are pivotal in diverse fields, particularly in mathematical problem-solving. This study introduces a novel approach for solving ordinary differential ...

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 tensor multigrid method and an iterative tensor multigrid method to solve the Sylvester tensor equations which may arise from the discretization of high order ...

Heat energy plays an essential role in numerous engineering applications, from thermal management in electronic devices to the design of efficient energy systems. Understanding and predicting the ...