Advance Numerical Techniques to Solve Linear and Nonlinear Differential Equations (River Publishers Series in Mathematical, Statistical and Computational Modelling for Engineering)

✍ Scribed by Geeta Arora (editor), Mangey Ram (editor)

• Publisher: River Publishers
• Year: 2024
• Tongue: English
• Leaves: 172
• Category: Library

✦ Synopsis

Real-world issues can be translated into the language and concepts of mathematics with the use of mathematical models. Models guided by differential equations with intuitive solutions can be used throughout engineering and the sciences. Almost any changing system may be described by a set of differential equations. They may be found just about anywhere you look in fields including physics, engineering, economics, sociology, biology, business, healthcare, etc. The nature of these equations has been investigated by several mathematicians over the course of hundreds of years and, consequently, numerous effective methods for solving them have been created. It is often impractical to find a purely analytical solution to a system described by a differential equation because either the system itself is too complex or the system being described is too vast. Numerical approaches and computer simulations are especially helpful in such systems.

The content provided in this book involves real-world examples, explores research challenges in numerical treatment, and demonstrates how to create new numerical methods for resolving problems. Theories and practical applications in the sciences and engineering are also discussed. Students of engineering and applied mathematics, as well as researchers and engineers who use computers to solve problems numerically or oversee those who do, will find this book focusing on advance numerical techniques to solve linear and nonlinear differential equations useful.

✦ Table of Contents

Cover
Half Title
Series
Title
Copyright
Contents
Preface
List of Figures
List of Tables
List of Contributors
List of Abbreviations
1 A Slow Varying Envelope of the Electric Field is Influenced by Integrability Conditions
1.1 Introduction
1.2 Solitary Wave Solutions
1.2.1 The Khater II method’s results
1.2.2 The Sardar sub-equation method’s results
1.3 Results and Discussion
1.4 Conclusion
2 Novel Cubic B-spline Based DQM for Studying Convection–Diffusion Type Equations in Extended Temporal Domains
2.1 Introduction
2.2 Portrayal of nHCB-DQM
2.3 Computation of Wt. Coeff ail(1) and ail(2)
2.4 The nHCB-DQM for the Class of C–D Eqn
2.5 Numerical Results and Discussion
2.6 Conclusion
3 Study of the Ranking-function-based Fuzzy Linear Fractional Programming Problem: Numerical Approaches
3.1 Introduction
3.2 Preliminaries
3.3 General Form of Fuzzy LFPP
3.4 Algorithm for the Solution of FLFPP with Trapezoidal Fuzzy Number TrpFN
3.5 Numerical Example
3.6 Conclusion
4 Orthogonal Collocation Approach for Solving Astrophysics Equations using Bessel Polynomials
4.1 Introduction
4.2 Bessel Collocation Method
4.3 Convergence Analysis
4.4 Numerical Examples
4.5 Conclusions
5 B-spline Basis Function and its Various Forms Explained Concisely
5.1 Introduction
5.1.1 Idea of spline
5.2 B-spline
5.2.1 Trigonometric B-spline
5.2.1.1 Three degree or cubic trigonometric B-spline
5.2.2 Hyperbolic B-spline
5.2.2.1 Cubic hyperbolic B-spline
5.2.3 Uniform algebraic trigonometric tension B-spline
5.2.4 Exponential B-spline
5.2.4.1 Exponential cubic B-spline
5.2.5 Quartic hyperbolic trigonometric B-spline
5.2.6 Quintic hyperbolic B-spline
5.2.7 Modified cubic UAH (uniform algebraic hyperbolic) tension B-spline
5.2.8 Modified cubic UAT tension B-spline
5.2.9 Quintic trigonometric B-spline
5.2.10 Quartic trigonometric differential
5.3 Equation Solved by the B-spline Basis Function
5.4 Conclusion
6 A Comparative Study: Modified Cubic B-spline-based DQM and Sixth-order CFDS for the Klein Gordon Equation
6.1 Introduction
6.2 Methodology
6.2.1 MCB-DQM
6.2.1.1 The weighting coefficients
6.2.2 CFDS6
6.3 Implementation of the Method
6.4 Results and Discussion
6.5 Conclusion
7 Sumudu ADM on Time-fractional 2D Coupled Burgers’ Equation: An Analytical Aspect
7.1 Introduction
7.2 Main Text Implementation of the Scheme
7.3 Examples and Calculation
7.4 Graphs and Discussion
7.5 Concluding Remarks
8 Physical and Dynamical Characterizations of the Wave’s Propagation in Plasma Physics and Crystal Lattice Theory
8.1 Introduction
8.2 GP model’s Traveling Wave Solutions
8.2.1 Solitary wave solutions
8.2.2 Solution’s accuracy
8.3 Soliton Solution’s Novelty
8.4 Conclusion
9 Numerical Solution of Fractional-order One-dimensional Differential Equations by using Laplace Transform with the Residual Power Series Method
9.1 Introduction
9.2 Preliminaries
9.3 Methodology
9.4 Numerical Solutions
9.5 Conclusion
Index
About the Editors