Santanu Saha Ray Libros

The book explores innovative analytical and numerical techniques for addressing partial and fractional differential equations. It highlights specific numerical methods, including Euler-Maruyama and strong-order Taylor methods, for solving stochastic point kinetic equations relevant to nuclear reactor dynamics. Additionally, it presents new exact solutions for a range of fractional differential equations, such as the time-fractional Burgers-Hopf equation and various (3+1)-dimensional equations, showcasing the depth and applicability of these methods in advanced mathematical contexts.

Stochastic partial differential equations (SPDEs) represent a significant advancement in modeling systems where parameters are uncertain, particularly in fields like physics and economics. These equations blend deterministic partial differential equations with stochastic processes, incorporating elements of both finite and infinite dimensions. The use of white noise, despite being a mathematical abstraction, effectively captures rapid random fluctuations, making SPDEs a powerful tool for understanding complex systems influenced by randomness.