Integral and Integro-Differential Equations: Wavelet-Based Numerical Methods [Hardcover]

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

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.?

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.

Features

• Employs wavelet approximation methods to solve a wide range of integral and integro-differential equations<l“)