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Title Advance numerical techniques to solve linear and nonlinear differential equations / editors, Geeta Arora, Mangey Ram
Published [United States] : River Publishers, [2024]


Description 1 online resource
Series River Publishers series in mathematical, statistical and computational modelling for engineering
River Publishers series in mathematical, statistical and computational modelling for engineering
Contents Preface ix List of Figures xi List of Tables xiii List of Contributors xv List of Abbreviations xvii 1 A Slow Varying Envelope of the Electric Field is Influenced by Integrability Conditions 1 1.1 Introduction 2 1.2 Solitary Wave Solutions 6 1.2.1 The Khater II method⁰́₉s results 6 1.2.2 The Sardar sub-equation method⁰́₉s results 8 1.3 Results and Discussion 15 1.4 Conclusion 15 2 Novel Cubic B-spline Based DQM for Studying Convection⁰́₃Diffusion Type Equations in Extended Temporal Domains 21 2.1 Introduction 22 2.2 Portrayal of nHCB-DQM 23 2.3 Computation of Wt. Coeff. a(1)il and a(2)il 25 2.4 The nHCB-DQM for the Class of C⁰́₃D Eqn 26 2.5 Numerical Results and Discussion 27 2.6 Conclusion 31 3 Study of the Ranking-function-based Fuzzy Linear Fractional Programming Problem: Numerical Approaches 37 3.1 Introduction 37 3.2 Preliminaries 38 3.3 General Form of Fuzzy LFPP 40 3.4 Algorithm for the Solution of FLFPP with Trapezoidal Fuzzy Number TrpFN 41 3.5 Numerical Example 41 3.6 Conclusion 43 4 Orthogonal Collocation Approach for Solving Astrophysics Equations using Bessel Polynomials 45 4.1 Introduction 45 4.2 Bessel Collocation Method 47 4.3 Convergence Analysis 55 4.4 Numerical Examples 56 4.5 Conclusions 59 5 B-spline Basis Function and its Various Forms Explained Concisely 63 5.1 Introduction 64 5.1.1 Idea of spline 64 5.2 B-spline 64 5.2.1 Trigonometric B-spline 68 Three degree or cubic trigonometric B-spline 68 5.2.2 Hyperbolic B-spline 69 Cubic hyperbolic B-spline 69 5.2.3 Uniform algebraic trigonometric tension B-spline 70 5.2.4 Exponential B-spline 72 Exponential cubic B-spline 73 5.2.5 Quartic hyperbolic trigonometric B-spline 74 5.2.6 Quintic hyperbolic B-spline 74 5.2.7 Modified cubic UAH (uniform algebraic hyperbolic) tension B-spline 76 5.2.8 Modified cubic UAT tension B-spline 77 5.2.9 Quintic trigonometric B-spline 78 5.2.10 Quartic trigonometric differential 79 5.3 Equation Solved by the B-spline Basis Function 79 5.4 Conclusion 80 6 A Comparative Study: Modified Cubic B-spline-based DQM and Sixth-order CFDS for the Klein⁸́₂Gordon Equation 85 6.1 Introduction 86 6.2 Methodology 87 6.2.1 MCB-DQM 88 The weighting coefficients 88 6.2.2 CFDS6 89 6.3 Implementation of the Method 91 6.4 Results and Discussion 91 6.5 Conclusion 97 7 Sumudu ADM on Time-fractional 2D Coupled Burgers⁰́₉ Equation: An Analytical Aspect 103 7.1 Introduction 103 7.2 Main Text Implementation of the Scheme 104 7.3 Examples and Calculation 106 7.4 Graphs and Discussion 113 7.5 Concluding Remarks 114 8 Physical and Dynamical Characterizations of the Wave⁰́₉s Propagation in Plasma Physics and Crystal Lattice Theory 117 8.1 Introduction 118 8.2 GP model⁰́₉s traveling wave solutions 122 8.2.1 Solitary wave solutions 122 8.2.2 Solution⁰́₉s accuracy 124 8.3 Soliton Solution⁰́₉s Novelty 124 8.4 Conclusion 129 9 Numerical Solution of Fractional-order One-dimensional Differential Equations by using a Laplace Transform with the Residual Power Series Method 135 9.1 Introduction 136 9.2 Preliminaries 137 9.3 Methodology 139 9.4 Numerical Solutions 141 9.5 Conclusion 145 Index 149 About the Editors 151
Summary 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
Notes Title details screen
Subject Differential equations, Linear -- Numerical solutions.
Differential equations, Nonlinear -- Numerical solutions.
Form Electronic book
Author Arora, Geeta, editor
Ram, Mangey, editor.
ISBN 9788770229869