Advance Numerical Techniques to Solve Linear and Nonlinear Differential Equations

Geeta Arora, Mangey Ram

• Publisher: River Publishers
• Year: 2024
• Print ISBN: 9788770229876
• eBook ISBN: 9781003811022
• Edition: 1
• Topic: Matematica
• Subtopic: Equazioni differenziali

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
• 2 Novel Cubic B-spline Based DQM for Studying Convection–Diffusion Type Equations in Extended Temporal Domains
• 3 Study of the Ranking-function-based Fuzzy Linear Fractional Programming Problem: Numerical Approaches
• 4 Orthogonal Collocation Approach for Solving Astrophysics Equations using Bessel Polynomials
• 5 B-spline Basis Function and its Various Forms Explained Concisely
• 6 A Comparative Study: Modified Cubic B-spline-based DQM and Sixth-order CFDS for the Klein−Gordon Equation
• 7 Sumudu ADM on Time-fractional 2D Coupled Burgers’ Equation: An Analytical Aspect
• 8 Physical and Dynamical Characterizations of the Wave’s Propagation in Plasma Physics and Crystal Lattice Theory
• 9 Numerical Solution of Fractional-order One-dimensional Differential Equations by using a Laplace Transform with the Residual Power Series Method
• Index
• About the Editors