Abstract: In this article, we study system of Riccati equations using the operational matrix method. This system is important since it has several applications in different areas such as random ...

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 ...

The author recounts a personal journey from focusing on astronomy to becoming deeply involved in climate change research, highlighting the disconnect between scientific understanding and societal ...

Are you struggling to solve quadratic equations? Look no further than the “Almighty Formula,” a powerful mathematical tool that can crack even the toughest quadratic puzzles. In this article, you will ...

State Key Laboratory of Genetic Engineering, School of Life Sciences, Human Phenome Institute, Zhangjiang Fudan International Innovation Center, Metabonomics and Systems Biology Laboratory at Shanghai ...

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, ...