Advanced Computational and Mathematical Approaches in Applied Differential Equations

Advanced Computational and Mathematical Approaches in Applied Differential Equations explores cutting-edge techniques and methodologies in solving complex differential equations, a cornerstone of mathematical modelling across science and engineering. This book bridges theory and application, offering advanced computational strategies and innovative mathematical insights to address real-world problems. Ideal for researchers, practitioners, and advanced students, it provides a comprehensive resource for tackling challenging applied differential equations with better precision and efficiency. Differential equations are fundamental to modelling complex systems, yet solving them often involves significant challenges due to their complexity and nonlinearity. This book equips readers with advanced tools and methodologies to overcome these challenges, providing innovative solutions that improve accuracy, efficiency, and applicability in real-world scenarios. Beginning with an overview that presents a unified framework defining the types of differential equations covered (e.g. ordinary, partial, fractional, fuzzy), then progressing to foundations and methods such as Lie symmetries, homotropy, Adomian, FEM, FDM, spectral, machine learning, fuzzy, and fractional derivatives, the book addresses both computational and mathematical dimensions, empowering readers to solve applied differential equations more effectively.