Initially, the mathematician would consider various factors and attempt to simplify the situation. Time becomes a crucial element, with a certain duration allocated for decision-making. A ...

Abstract: It is noteworthy that the Sylvester equation plays a pivotal role in the field of industrial intelligence control. To meet the demands of real-time applications, temporal-dependent Sylvester ...

The year 2022 marked the 200 th anniversary of the first appearance of the Navier–Stokes equation, a landmark in Fluid Dynamics introduced by Claude-Louis Navier in 1822. This equation revolutionized ...

Abstract: The purpose of this work is to explore the internal resonance exhibited by the heave-pitch coupled motion of a classic Spar platform via an equivalent analog circuit method. First, the pitch ...

In this work, we establish new exact solutions for the Hirota-Satsuma equations. New approach for the tanh is used and extended tanh methods to construct traveling wave solutions in terms of a ...

On his 80th birthday, inside a grand Parisian villa, a wealthy grandfather catches his granddaughter stealing a rare pearl from his collection. But instead of reacting with anger, the moment opens a ...

State Key Laboratory of Coordination Chemistry, Key Laboratory of Mesoscopic Chemistry of Ministry of Education, New Cornerstone Science Laboratory, School of Chemistry and Chemical Engineering, ...

New research details an intriguing new way to solve "unsolvable" algebra problems that go beyond the fourth degree – something that has generally been deemed impossible using traditional methods for ...

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 ...