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 modeling across science and engineering. The book bridges theory and application, offering advanced computational strategies and innovative mathematical insights to address real-world problems.

Beginning with an overview that presents a unified framework that defines the types of differential equations covered (e.g. ordinary, partial, fractional, fuzzy), the book then progresses to foundations and methods such as Lie symmetries, homotopy, Adomian, FEM, FDM, spectral, machine learning, fuzzy, and fractional derivatives, addressing both computational and mathematical dimensions.

Significance of Differential Equations

Differential equations are fundamental to modeling complex systems, yet solving them often involves significant challenges due to their complexity and nonlinearity. The 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.

Target Audience and Content

Ideal for researchers, practitioners, and advanced students, it provides a comprehensive resource for tackling challenging applied differential equations with better precision and efficiency.

- Presents a systematic approach to handling differential equations through computational and mathematical methods

- Includes analytical, semi-analytical, and numerical methods, along with algorithms for practical implementation

- Provides readers with easy-to-follow examples of generalized systems governed by linear or non-linear differential equations

- Includes extensive case studies that demonstrate the power of mathematical modeling in solving a variety of scientific, engineering, and advanced computational implementations, along with pseudocode, MATLAB, and Python code examples