Abstract: Analytically solving complex or large-scale differential equations is often difficult or even impossible, making numerical integration methods indispensable. However, as all numerical ...

Abstract: Based on deep neural network, elliptic partial differential equations in complex regions are solved. Accurate and effective strategies and numerical methods for elliptic partial differential ...

A high-performance Python package implementing the Quasi-Steady State (QSS) method for solving stiff ordinary differential equations, with particular focus on combustion chemistry applications. This ...

This study introduces a relatively new numerical technique for solving one-dimensional Fisher’s equation. The proposed numerical technique is a simple direct meshless method, which is based on the ...

Fractional differential equations have recently gained popularity due to their ability to simulate a wide range of complex processes in various fields, including engineering, physics, biology, and ...

Adequate mathematical modeling is the key to success for many real-world projects in engineering, medicine, and other applied areas. Once a well-suited model is established, it can be thoroughly ...

Handling stiff vs. non-stiff systems with appropriate solvers. Adaptive step-size control to balance accuracy and efficiency. High-precision numerical integration for real-world simulations. Finite ...

1 College of Mathematics and Information Science, Nanchang Hangkong University, Nanchang, China. 2 School of Statistics and Data Science, Jiangxi University of Finance and Economics, Nanchang, China.

This repository contains a collection of Python scripts and Jupyter notebooks for practicing numerical methods commonly used in scientific computing and engineering applications. The exercises cover a ...

This paper presents a new approach for finding exact solutions to certain classes of nonlinear partial differential equations (NLPDEs) by combining the variation of parameters method with classical ...

In the world of mathematics and scientific computing, numerical methods are invaluable tools that bridge the gap between theory and real-world problem-solving. They are the workhorses behind ...

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 ...