Advanced Numerical Methods for Differential Equations - Info and Reading Options

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Cover -- Half Title -- Series Page -- Title Page -- Copyright Page -- Contents -- Preface -- About the Author -- Chapter 1: Stability and Convergence Analysis of Numerical Scheme for the Generalized Fractional Diffusion-Reaction Equation -- 1.1. Introduction -- 1.2. Fractional Derivatives Review -- 1.3. Existence and Uniqueness Via Banach Fixed Theorem -- 1.4. Numerical Scheme of the Fractional Diffusion Reaction Equation -- 1.5. Stability Analysis of the Numerical Approximation -- 1.6. Convergence Analysis of the Numerical Approximation -- 1.7. The Graphics with the Numerical Scheme -- 1.8. Conclusion -- References -- Chapter 2: Studying on the Complex and Mixed Dark-Bright Travelling Wave Solutions of the Generalized KP-BBM Equation -- 2.1. Introduction -- 2.2. The SGEM -- 2.3. Applications of SGEM and Mathematical Analysis -- 2.3.1. Investigation of Generalized KP-BBM Equation -- 2.4. Conclusions -- References -- Chapter 3: Abundant Computational and Numerical Solutions of the Fractional Quantum Version of the Relativistic Energy-Momentum Relation -- 3.1. Introduction -- 3.2. Analytical Explicit Wave Solutions -- 3.2.1. Extended exp ( -f(X)) Expansion Method -- 3.2.2. Extended Fan Expansion Method -- 3.2.3. Extended (G0 G ) Expansion Method -- 3.2.4. Improved F-expansion Method -- 3.2.5. Modified Khater Method -- 3.3. Stability -- 3.4. Numerical Solutions -- 3.4.1. Semi-Analytical Solutions -- 3.4.2. Numerical Solutions -- 3.4.2.1. Cubic B-Spline -- 3.4.2.2. Quantic-B-spline -- 3.4.2.3. Septic B-Spline -- 3.5. Figures Representation -- 3.6. Conclusion -- References -- Chapter 4: Applications of Conserved Schemes for Solving Ultra-Relativistic Euler Equations -- 4.1. Introduction -- 4.2. The URE Equations -- 4.2.1. The (p, u) Subsystem -- 4.3. The Numerical Schemes -- 4.3.1. Cone Grid Scheme -- 4.3.2. The Structure of Numerical Solutions

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