Advances in Computational Methods and Modeling for Science and Engineering

1st Edition - February 4, 2025
Editors: Hari M Srivastava, Geeta Arora, Firdous Shah
Language: English
Paperback ISBN:
9 7 8 - 0 - 4 4 3 - 3 0 0 1 2 - 7
eBook ISBN:
9 7 8 - 0 - 4 4 3 - 3 0 0 1 3 - 4

Advances in Computational Methods and Modelling in Science and Engineering explores the application of computational techniques and modeling approaches in science and engine… Read more

Advances in Computational Methods and Modeling for Science and Engineering

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Advances in Computational Methods and Modelling in Science and Engineering explores the application of computational techniques and modeling approaches in science and engineering, providing practical knowledge and skills for tackling complex problems using numerical simulations and data analysis. This book addresses the need for a cohesive and up-to-date resource in the rapidly evolving field of computational methods. It consolidates diverse topics, serving as a one-stop guide for individuals seeking a comprehensive understanding of the subject matter. Sections focus on mathematical techniques that provide global solutions for models arising in engineering and scientific research applications by considering their long-term benefits.

The mathematical treatment of these models is very helpful in understanding these models and their real-world applications. The methods and modeling techniques presented are useful for mathematicians, engineers, scientists, and researchers working on the mathematical treatment of models in a wide range of applications, including disciplines such as engineering, physics, chemistry, computer science, and applied mathematics.

Title of Book
Cover image
Title page
Table of Contents
Copyright
Contributors
About the editors
A: Computational methods
Chapter 1: Exploring new traveling and solitary wave solutions of conformable fractional (3+1)-D BLMP differential equations
1.1. Introduction
1.2. Description of the mERF method
1.3. Application to conformable fractional (3+1)-D BLMP models
1.4. Physical explanation of solutions
1.5. Conclusion
Chapter 2: Numerical investigation of fractional-order brain tumor growth model via Fibonacci wavelets
2.1. Introduction
2.2. Formulation of the fractional-order brain tumor growth model
2.2.1. Basics of fractional calculus
2.2.2. Formulation of the time-fractional brain tumor growth model
2.3. Wavelets and function approximation
2.3.1. Fibonacci polynomials and wavelets
2.3.2. Conventional Haar wavelets
2.3.3. Operational matrices associated with Fibonacci and Haar wavelets
2.3.4. Quasi-linearization technique for linearization
2.4. Method of solution via Fibonacci wavelets
2.4.1. Solution of the brain tumor growth model via Fibonacci wavelets
2.4.2. Solution of the brain tumor growth model via Haar wavelets
2.5. Numerical simulation and discussion
2.6. Epilogue
Chapter 3: Application of dynamical system analysis in cosmology
3.1. Introduction
3.2. Dynamical systems
3.2.1. Introduction to dynamical systems
3.3. Modern cosmology
3.3.1. Friedmann model
3.4. Application of dynamical systems
3.4.1. ΛCDM
3.4.2. Canonical scalar field
3.5. Conclusion
Chapter 4: Polynomial-based fractional methods of wavelets and their applications
4.1. Introduction
4.2. Preliminaries
4.3. Fractional-order Fibonacci wavelets
4.4. Description of the fractional-Fibonacci wavelet scheme
4.5. Numerical examples
4.6. Shifted fractional-order Gegenbauer wavelet
4.7. Operational matrix of fractional-order integration of SFGBW
4.8. Applications and numerical simulations
4.9. Conclusion
Chapter 5: A numerical study of exponential modified cubic B-spline for solving nonlinear Fisher's equation
5.1. Introduction
5.2. Numerical scheme
5.3. Methodology implementation and discussions
5.4. Conclusions
Chapter 6: Numerical simulation of symmetric regularized long wave equations arising in mathematical physics
6.1. Introduction
6.2. Trigonometric cubic B-splines and collocation method
6.2.1. Trigonometric cubic B-splines
6.2.2. Collocation method
6.3. Discretization
6.3.1. Initial solution
6.4. Numerical simulations
6.4.1. Single solitary wave motion
6.4.2. Example 2: Collision of two solitons
6.5. Conclusion
Chapter 7: Comparison of exponential and trigonometric B-spline collocation techniques for simulation of singular perturbed delay differential equations
7.1. Introduction
7.2. Problem statement
7.3. Existence of solutions and selection of a mesh
7.4. Implementation of collocation methods
7.5. Anatomy of convergence
7.6. Numerical examples
7.7. Discussion of numerical examples
7.8. Conclusion
Chapter 8: A systematic study on diversified Newtonian and non-Newtonian fluids via numerous mathematical techniques
8.1. Introduction
8.2. Implementation of regime
8.3. Results and discussion
8.4. Summary of observations
8.5. Conclusion
Chapter 9: Computational analysis for the stress–strength on the reliability model
9.1. Introduction
9.2. Probability of disaster (α)
9.3. Numerical values for the probability of disaster
9.4. Stress–strength reliability P=Pr(Y>X)
9.5. Interpretive study
9.6. Case Study
9.7. Conclusion
Chapter 10: Instability of Casson fluid–viscous fluid interfaces
10.1. Introduction
10.2. Problem formulated
10.3. Boundary and interfacial conditions
10.3.1. Boundary conditions
10.3.2. Interfacial conditions
10.4. Stability analysis
10.4.1. Equilibrium state
10.4.2. Perturbed state
10.5. Dispersion relationship
10.6. Results and discussions
10.7. Conclusions
Chapter 11: Remarks on nonlinear fractional differential equations
11.1. Generalized Abel integral equations
11.1.1. Preliminaries
11.1.2. Main results
11.1.3. An illustrative example
11.1.4. Conclusion
11.2. The fractional nonlinear problem with an integral boundary condition
11.2.1. Introduction
11.2.2. Background
11.2.3. Existence and uniqueness
11.2.4. Examples
11.2.5. Conclusion
11.3. Uniqueness of Hadamard-type integral equations
11.3.1. Introduction
11.3.2. Main results
11.3.3. Conclusion
11.4. Summary
Funding
Chapter 12: Exploring chaotic dynamics in a modified fractional system with the Atangana–Baleanu operator
12.1. Introduction
12.2. Preliminary concepts
12.3. The fractional chaotic system
12.4. Approximation of the Atangana–Baleanu fractional derivative
12.5. Simulation results
12.6. Numerical analysis
12.6.1. Equilibria
12.6.2. Jacobean matrix and stability
12.6.3. Lyapunov exponents
12.7. Impact of initial conditions
12.8. Conclusion
CRediT authorship contribution statement
Funding
Chapter 13: Impact of viscous correction on the viscoelastic potential flow analysis of the Rayleigh–Taylor instability
13.1. Introduction
13.2. Mathematical formulation and boundary conditions
13.2.1. Boundary conditions
13.2.2. Stability analysis
13.2.3. Contribution by pressure correction terms
13.3. Dispersion relationship
13.4. Results and discussion
13.4.1. A comparative analysis with (Shukla and Awasthi [17])
13.4.2. Impact of the Atwood number
13.4.3. Impact of Rivlin–Ericksen fluid thickness
13.4.4. Impact of Weber number
13.4.5. Impact of the Reynolds number
13.4.6. Impact of viscoelasticity
13.4.7. Impact of the Froude number
13.5. Conclusion
Chapter 14: Finite element modeling of MHD flow in alveolar ducts
14.1. Introduction
14.2. Problem formulation
14.3. Finite element method
14.3.1. Galerkin approximation with variational formulations
14.3.2. Time stepping
14.4. Numerical results and discussion
14.5. Conclusions
B: Mathematical modeling and optimization
Chapter 15: The fractional-order Lotka–Volterra competition model: an analysis with the additive Allee effect
15.1. Introduction
15.2. Mathematical model
15.3. Mathematical preliminaries
15.4. Mathematical analysis
15.4.1. Uniqueness of the solution
15.4.2. Positivity of the solutions
15.4.3. Uniform boundedness of the solutions
15.5. Existence and stability conditions of equilibrium points
15.5.1. Equilibrium points
15.5.2. Stability analysis
15.6. Numerical simulations
15.7. Conclusion
Chapter 16: Modeling and analyzing delay in plant responses under toxicity
16.1. Introduction
16.2. Mathematical model
16.3. Analysis of the model
16.3.1. Boundedness of the dynamical system
16.3.2. Positivity of solution
16.3.3. Equilibrium point of the system
16.3.4. Biological interpation of the dynamical system
16.4. Sensitivity analysis of the dynamical model
16.4.1. Sensitivity analysis w.r.t r2
16.4.2. Sensitivity analysis w.r.t r5
16.5. Numerical example
16.5.1. Results & discussion
16.6. Conclusion
Appendix 16.A.
Appendix 16.B.
Appendix 16.C.
Chapter 17: Mathematical modeling of coral–algal competition under environmental pressures in aquatic ecosystems: a review
17.1. Introduction
17.2. Basic model of the interaction between algae and corals
17.3. Other models depicting the coral–algal relationship
17.4. Modeling coral–algal relationship under toxin-induced coral death
17.5. Modeling coral–algal relationship under climate change
17.6. Modeling the role of herbivorous fishes in coral–algal relationship
17.7. Discussion
17.8. Conclusion
Chapter 18: Effect of time delay on directional and stability analysis of plant competition for allelochemicals study
18.1. Introduction
18.2. Mathematical model
18.3. Boundedness
18.4. Positivity of the solutions
18.5. Equilibrium points
18.6. Local stability of the equilibrium E⁎(P1⁎,P2⁎)
18.7. Global stability of the equilibrium E⁎(P1⁎,P2⁎)
18.8. Direction and stability of Hopf-bifurcating solution
18.9. Numerical example
18.10. Result and discussion
18.11. Conclusion
CRediT authorship contribution statement
Formatting of funding sources
Chapter 19: Harnessing the potentials of machine learning models in Alzheimer's disease prediction and detection
19.1. Introduction
19.2. Taxonomy
19.2.1. ADHD detection and prediction using machine learning (ML) based on neuroimaging
19.2.2. Feature-based approaches
19.3. Conclusion
Chapter 20: Impact of deforestation and environmental degradation on Nipah virus outbreaks: a critical review
20.1. Introduction
20.2. Correlation in trends in human population growth and forest-cover decline
20.2.1. Human population explosion
20.2.2. Human population growth and environmental degradation
20.3. Effect of deforestation on wildlife habitat
20.4. Wildlife habitat destruction and zoonotic spillover
20.5. Possible correlation between environment degradation on NiV outbreaks
20.6. Conclusion
Chapter 21: Current advances in data-driven modeling and computational tools for novel materials
21.1. Introduction
21.2. Computational modeling and various methods for materials properties
21.2.1. Molecular dynamics
21.2.2. Density functional theory
21.2.3. Finite element method
21.2.4. Monte Carlo simulation
21.3. Current advances in data-driven modeling
21.4. Conclusion
Chapter 22: Onset of bioconvection in the presence of magnetic nanoparticles and gyrotactic microorganisms in porous media
22.1. Introduction
22.2. Physical model of the problem
22.3. Mathematical representation of the problem
22.4. The steady-state solution
22.5. Linearization
22.6. Results and discussion
22.7. Conclusion
Chapter 23: Predicting diabetes using artificial neural networks and K-nearest neighbors
23.1. Introduction
23.2. Diabetes as a chronic metabolic disorder
23.2.1. Role of machine learning in diabetes prediction
23.3. Methodology
23.3.1. Dataset and preprocessing
23.3.2. K-nearest neighbors (KNN)
23.3.3. Artificial neural networks (ANN)
23.4. Performance analysis
23.4.1. Performance analysis of the KNN model
23.4.2. Performance analysis of ANN model
23.5. Results and discussion
23.6. Conclusion
Chapter 24: Real coded GA for finding stable structures of two small molecules
24.1. Introduction
24.2. Problem discussion
24.2.1. Finding a stable conformation for pseudoethane
24.2.2. Finding stable conformation for the 1,2,3-trichloro-1-fluoro-propane molecule
24.3. Problem complexity
24.3.1. Real coded genetic algorithms
24.3.2. Parameter settings
24.3.3. Computational results and discussion
24.3.4. Pseudoethane
24.3.5. 1,2,3-trichloro-1-fluoro-propane
24.4. Conclusions
Chapter 25: Cost optimization of a batch retrial queue with a working vacation
25.1. Introduction
25.1.1. Retrial queue
25.2. Literature review
25.3. Description of the model
25.3.1. Practical application of this model
25.4. Steady-state analysis
25.4.1. Notations & probabilities
25.4.2. Steady-state equations
25.4.3. Steady-state solutions
25.5. Performance measures of the system
25.5.1. State probabilities of the system
25.5.2. Average size of system and orbit
25.5.3. Reliability measures
25.6. Numerical analysis
25.7. Conclusion
Chapter 26: Future now: unleashing the potentials of machine learning algorithms in 6G
26.1. Introduction
26.2. Preliminaries of 6G
26.2.1. Globular trends towards 6G
26.2.2. Requirements
26.2.3. Candidate technologies
26.2.4. Milestones in development of 6G
26.3. Machine learning algorithms for 6G
26.3.1. Machine learning algorithms for latency minimization
26.3.2. Machine learning algorithms that improve energy efficiency
26.3.3. Machine learning algorithms for RAT selection
26.4. Conclusion
Index

Hari M Srivastava

Dr. Hari M. Srivastava is Professor Emeritus in the Department of Mathematics and Statistics at the University of Victoria, British Columbia, Canada. He earned his Ph.D. degree in 1965 while he was a full-time member of the teaching faculty at the Jai Narain Vyas University of Jodhpur, India. Dr. Srivastava has held (and continues to hold) numerous Visiting, Honorary and Chair Professorships at many universities and research institutes in diﬀerent parts of the world. Having received several D.Sc. (honoris causa) degrees as well as honorary memberships and fellowships of many scientiﬁc academies and scientiﬁc societies around the world, he is also actively associated editorially with numerous international scientiﬁc research journals as an Honorary or Advisory Editor or as an Editorial Board Member. He has also edited many Special Issues of scientiﬁc research journals as the Lead or Joint Guest Editor, including the MDPI journal Axioms, Mathematics, and Symmetry, the Elsevier journals, Journal of Computational and Applied Mathematics, Applied Mathematics and Computation, Chaos, Solitons & Fractals, Alexandria Engineering Journal, and Journal of King Saud University – Science, the Wiley journal, Mathematical Methods in the Applied Sciences, the Springer journals, Advances in Diﬀerence Equations, Journal of Inequalities and Applications, Fixed Point Theory and Applications, and Boundary Value Problems, the American Institute of Physics journal, Chaos: An Interdisciplinary Journal of Nonlinear Science, and the American Institute of Mathematical Sciences journal, AIMS Mathematics, among many others. Dr. Srivastava has been a Clarivate Analytics (Web of Science) Highly-Cited Researcher since 2015. Dr. Srivastava’s research interests include several areas of Pure and Applied Mathematical Sciences, such as Real and Complex Analysis, Fractional Calculus and Its Applications, Integral Equations and Transforms, Higher Transcendental Functions and Their Applications, q-Series and q-Polynomials, Analytic Number Theory, Analytic and Geometric Inequalities, Probability and Statistics, and Inventory Modeling and Optimization. He has published 36 books, monographs, and edited volumes, 36 book (and encyclopedia) chapters, 48 papers in international conference proceedings, and more than 1450 peer-reviewed international scientiﬁc research journal articles, as well as Forewords and Prefaces to many books and journals.

Affiliations and expertise

Professor Emeritus, Department of Mathematics and Statistics, University of Victoria, British Columbia, Canada

Geeta Arora

Dr. Geeta Arora is currently a Professor at the Department of Mathematics, Lovely Professional University, Punjab, India. She earned her Ph.D. degree from IIT Roorkee, India in 2011. Her research interests include Numerical Analysis, Partial Differential Equations and Wavelets. She has over eleven years of teaching experience and published around 50 research papers in both international and national Journals. She has authored 10 book chapters in national and international publications. Dr. Arora is the author of a two introductory mathematics books, Quick Calculations in Mathematics and Essential Statistics. Her area of applied research is the development of numerical methods and statistics.

Affiliations and expertise

Lovely Professional University, India

Firdous Shah

Dr. Firdous A. Shah earned his post-graduate degree in pure mathematics from the University of Kashmir and a PhD in applied mathematics from the Central University, Jamia Millia Islamia, New Delhi, India. He is an associate professor of mathematics at the University of Kashmir, South Campus, India. His research interests include the theory of wavelets, time-frequency analysis, abstract harmonic analysis, sampling theory and applications of wavelets to signal processing and mathematical biology. He is the author/co-author of over 200 journal articles and has co-authored two books with Prof. Lokenath Debnath (University of Texas) on wavelet transforms and their applications, published by Birkhauser, Springer. Recently, he has authored another book entitled Wavelet Transforms: Kith and Kin, published by CRC Press. He has received numerous research grants from NBHM and SERB-DST, Govt. of India. He serves as an editorial board member of several reputed journals and is a lifetime member of several academic societies.

Affiliations and expertise

University of Kashmir, India

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Advances in Computational Methods and Modeling for Science and Engineering

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Hari M Srivastava

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