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Full Description
This book provides a comprehensive study of numerical techniques for solving integral and integro-differential equations using wavelet-based approximation methods. It combines both theoretical insights and practical applications, focusing on integer- and fractional-order equations, including those with weakly singular kernels. Starting with key definitions and theorems from integral equations and fractional calculus, the book establishes a clear mathematical framework. It then introduces wavelet-based schemes for approximating solutions, with a particular focus on convergence, stability, and error analysis. Each chapter is enriched with numerical examples, graphs, and tables that demonstrate the accuracy and computational efficiency of the proposed methods.
Employs wavelet approximation methods to solve a wide range of integral and integro-differential equations
Expands the scope of applicable equations by covering both classical and fractional-order models
Illustrates the effectiveness of wavelet methods in handling weakly singular kernels through worked-out examples
Provides rigorous theoretical validation for the accuracy and reliability of each method.
This book is intended for postgraduate students, researchers, and professionals in mathematics, engineering, and applied sciences who seek modern computational techniques for solving integral and integro-differential equations.
Contents
1. Preliminaries of Integral Equations and Fractional Calculus 2. Wavelet Methods 3. Numerical Solutions of Two-Dimensional Fredhom Integral Equations of Second Kind 4. Numerical Solutions of Two-Dimensional Volterra Integral Equations 5. Numerical Solutions of Linear and Nonlinear Volterra Integro-Differential Equations 6. Numerical Solutions of Volterra Weakly Singular Partial Integro-Differential Equations 7. Numerical Solutions of Pantograph Volterra Delay-Integro-Differential Equations 8. Numerical Solutions of Fractional Order Integro-Differential Equations with Weakly Singular Kernels 9. Numerical Solutions of Fractional Order Integro-Differential Equations
