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 ...

This collection of Julia functions is an attemp to implement high performance numerical software to solve several classes of Lyapunov, Sylvester and Riccati matrix equations at a performance level ...

School of Chemistry, University of St. Andrews, North Haugh, St Andrews KY16 9ST, United Kingdom ...

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 ...

A matrix is a rectangular array of numbers, symbols, or expressions arranged in rows and columns. They are a crucial part of linear algebra and have various applications in fields like engineering, ...

Breakthroughs in the realm of optoelectronic circuits, demonstrating the power of PSPICE software in solving nonlinear equations for advanced electronics. Software models for Si and GaAs pin ...

Luis Caffarelli has won the 2023 Abel prize, unofficially called the Nobel prize for mathematics, for his work on a class of equations that describe many real-world physical systems, from melting ice ...