Showing results for "Computational Methods for Linear Integral Equations German"

This book deals with the numerical solution of integral equations based on approximation of functions and the authors apply wavelet approximation to the unknown function of integral equations. The book's goal is to categorize the selected methods and assess their accuracy and efficiency.

This book combines theory, applications, and numerical methods, and covers each of these fields with the same weight. In order to make the book accessible to mathematicians, physicists, and engineers alike, the author has made it as self-contained as possible, requiring only a solid foundation in differential and integral calculus. The functional analysis which is necessary for an adequate treatment of the theory and the numerical solution of integral equations is developed within the book...

Readable and systematic, this volume offers coherent presentations of not only the general theory of linear equations with a single integration, but also of applications to differential equations, the calculus of variations, and special areas in mathematical physics. Topics include the solution of Fredholm’s equation expressed as a ratio of two integral series in lambda, free and constrained vibrations of an elastic string, and auxiliary theorems on harmonic functions. Discussion of the Hi...

This book provides ideas for implementing Wolfram Mathematica to solve linear integral equations. The book introduces necessary theoretical information about exact and numerical methods of solving integral equations. Every method is supplied with a large number of detailed solutions in Wolfram Mathematica. In addition, the book includes tasks for individual study.This book is a supplement for students studying “Integral Equations”. In addition, the structure of the book with individ...

The recent appearance of wavelets as a new computational tool in applied mathematics has given a new impetus to the field of numerical analysis of Fredholm integral equations. This book gives an account of the state of the art in the study of fast multiscale methods for solving these equations based on wavelets. The authors begin by introducing essential concepts and describing conventional numerical methods. They then develop fast algorithms and apply these to solving linear, nonlinear Fr...

Advanced Computational and Mathematical Approaches in Applied Differential Equations explores cutting-edge techniques and methodologies in solving complex differential equations, a cornerstone of mathematical modeling across science and engineering. The book bridges theory and application, offering advanced computational strategies and innovative mathematical insights to address real-world problems. Beginning with an overview that presents a unified framework that defines the types of diff...

Modern Computational Methods for Fractional Differential Equations provides a comprehensive introduction to the fundamentals of fractional calculus. Covering a range of analytical and numerical methods specifically designed for fractional calculus problems, the book explains the step-by-step implementation and computational aspects of these methods. Readers of this book should feel empowered to effectively apply analytical and numerical techniques to solve fractional calcu...

This book describes a second-generation force-based method emerging from a general formulation where the partial differential equations of elasticity are replaced by equivalent algebraic equations. These algebraic equations of linear elasticity can be used to solve statically indeterminate problems inreduced forms that define either the new second-generation force-based approach or a new displacement-based approach. The new force-based method can serve as the basis for teaching stu...

Inequalities for Differential and Integral Equations has long been needed; it contains material which is hard to find in other books. Written by a major contributor to the field, this comprehensive resource contains many inequalities which have only recently appeared in the literature and which can be used as powerful tools in the development of applications in the theory of new classes of differential and integral equations. For researchers working in this area, it will be a valuable sour...

This book presents methods for the computational solution of some important problems of linear algebra: linear systems, linear least squares problems, eigenvalue problems, and linear programming problems. The book also includes a chapter on the fast Fourier transform and a very practical introduction to the solution of linear algebra problems on modern supercomputers.The book contains the relevant theory for most of the methods employed. It also emphasizes the practical aspects involved in...

This book presents recent mathematical methods in the area of inverse problems in imaging with a particular focus on the computational aspects and applications. The formulation of inverse problems in imaging requires accurate mathematical modeling in order to preserve the significant features of the image. The book describes computational methods to efficiently address these problems based on new optimization algorithms for smooth and nonsmooth convex minimization, on the use of structured...

One of the current main challenges in the area of scientific computing is the design and implementation of accurate numerical models for complex physical systems which are described by time dependent coupled systems of nonlinear PDEs. This volume integrates the works of experts in computational mathematics and its applications, with a focus on modern algorithms which are at the heart of accurate modeling: adaptive finite element methods, conservative finite difference methods and finite vo...