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, homotropy, Adomian, FEM, FDM, spectral, machine learning, fuzzy, and fractional derivatives, addressing both computational and mathematical dimensions.
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. Ideal for researchers, practitioners, and advanced students, it provides a comprehensive resource for tackling challenging applied differential equations with better precision and efficiency.
1. Introduction - p. xxvii 2. 1: Thermal diffusion and nonlinear radiation analysis of magnetohydrodynamics chemically reactive nanofluid flow on a stretching sheet - p. 1 3. 2: Solitary wave solution of generalized Boussinesq equation in fuzzy environment - p. 29 4. 3: Implicit cubic spline methods for solving intuitionistic fuzzy parabolic partial differential equations - p. 51 5. 4: On the analysis of the three-species food chain model involving fractional derivatives with nonsingular kernels - p. 67 6. 5: Uncertain dynamic responses of imprecisely defined beam fractionally damped beam subject to external loads using double parametric form-based homotopy analysis method - p. 93 7. 6: A mathematical model of solute transfer through a permeable channel: impact of viscosity - p. 117 8. 7: Effect of viscosity variation on exponential slider bearing lubrication - p. 131 9. 8: Mathematical model of velocity slip on flow in a channel with permeable walls - p. 147 10. 9: Stagnation point flow of trihybrid nanofluid past a shrinking sheet with induced magnetic effects - p. 159 11. 10: Semianalytical approach for solving Burgers equation by Sawi transform coupled with Adomian decomposition method - p. 173 12. 11: Parametric mathematical programs with vanishing constraints: sensitivity analysis - p. 189 13. 12: Optimizing IFS parameters of rational fractal linear splines with a memory-efficient quasi-Newton method for time series forecasting - p. 221 14. 13: Structure and arboricity of (k−r,k)-trees - p. 237 15. 14: Optimal control of a tumor-immune model considering targeted chemotherapy - p. 245 16. 15: Quantitative analysis of structural vibration problems by using modified physics-informed neural networks - p. 259 17. Index - p. 279
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, homotropy, Adomian, FEM, FDM, spectral, machine learning, fuzzy, and fractional derivatives, addressing both computational and mathematical dimensions.
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. Ideal for researchers, practitioners, and advanced students, it provides a comprehensive resource for tackling challenging applied differential equations with better precision and efficiency.
1. Introduction - p. xxvii 2. 1: Thermal diffusion and nonlinear radiation analysis of magnetohydrodynamics chemically reactive nanofluid flow on a stretching sheet - p. 1 3. 2: Solitary wave solution of generalized Boussinesq equation in fuzzy environment - p. 29 4. 3: Implicit cubic spline methods for solving intuitionistic fuzzy parabolic partial differential equations - p. 51 5. 4: On the analysis of the three-species food chain model involving fractional derivatives with nonsingular kernels - p. 67 6. 5: Uncertain dynamic responses of imprecisely defined beam fractionally damped beam subject to external loads using double parametric form-based homotopy analysis method - p. 93 7. 6: A mathematical model of solute transfer through a permeable channel: impact of viscosity - p. 117 8. 7: Effect of viscosity variation on exponential slider bearing lubrication - p. 131 9. 8: Mathematical model of velocity slip on flow in a channel with permeable walls - p. 147 10. 9: Stagnation point flow of trihybrid nanofluid past a shrinking sheet with induced magnetic effects - p. 159 11. 10: Semianalytical approach for solving Burgers equation by Sawi transform coupled with Adomian decomposition method - p. 173 12. 11: Parametric mathematical programs with vanishing constraints: sensitivity analysis - p. 189 13. 12: Optimizing IFS parameters of rational fractal linear splines with a memory-efficient quasi-Newton method for time series forecasting - p. 221 14. 13: Structure and arboricity of (k−r,k)-trees - p. 237 15. 14: Optimal control of a tumor-immune model considering targeted chemotherapy - p. 245 16. 15: Quantitative analysis of structural vibration problems by using modified physics-informed neural networks - p. 259 17. Index - p. 279
