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Linear and Nonlinear Integral Equations: Methods and Applications is a self-contained book divided into two parts. Part I offers a comprehensive and systematic treatment of linear integral equations of the first and second kinds.
Chebyshev polynomials for solving two dimensional linear and nonlinear integral equations of the second kind. In this paper, an efficient method is presented for solving two dimensional Fredholm and Volterra integral equations of the second kind. Chebyshev polynomials are applied to approximate a solution for these integral equations. This method transforms the integral equation to algebraic equations with unknown Chebyshev coefficients. The high accuracy of this method is verified through some numerical examples. Mathematical subject classification: 65R20, 41A50, 41A55, 65M Key words: Chebyshev polynomials, two dimensional integral equations, collocation method.
Integral equations are one of the most useful mathematical tools in both pure and applied mathematics. They have enormous applications in many real problems. Many initial and boundary value problems associated with ordinary differential equation ODE and partial differential equation PDE can be transformed into problems of solving some approximate integral equations. Indeed, modeling such problems using integral equations with the exact parameters is not only easy but also impossible in the real problems. For this purpose, one way is using some uncertainty measures for handling such lack of information.
Subscribe to our Newsletter and get informed about new publication regulary and special discounts for subscribers! Full Text PDF. This work is licensed under a Creative Commons Attribution 4. Hashmi, N. Khan, S. Iqbal, Optimal homotopy asymptotic method for solving nonlinear Fredholm integral equations of second kind, Appl.
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It seems that you're in Germany. We have a dedicated site for Germany. Linear and Nonlinear Integral Equations: Methods and Applications is a self-contained book divided into two parts. Part I offers a comprehensive and systematic treatment of linear integral equations of the first and second kinds. The text brings together newly developed methods to reinforce and complement the existing procedures for solving linear integral equations. The Volterra integral and integro-differential equations, the Fredholm integral and integro-differential equations, the Volterra-Fredholm integral equations, singular and weakly singular integral equations, and systems of these equations, are handled in this part by using many different computational schemes. Selected worked-through examples and exercises will guide readers through the text.
takes an important place in solving the linear and nonlinear integral many diﬀerent methods to solve the integral equations ()–(). [44] M.A. Abdou, Integral equation with Macdonald kernel and its application to a.
MSC : 35A01, 32K Citation: Pakhshan M. Hasan, Nejmaddin A.
Skip to search form Skip to main content You are currently offline. Some features of the site may not work correctly. Wazwaz Published Mathematics. Linear and Nonlinear Integral Equations: Methods and Applications is a self-contained book divided into two parts. Part I offers a comprehensive and systematic treatment of linear integral equations of the first and second kinds.
From the reviews: "This is a useful book that concerns solution methods for integral equations of Volterra and Fredholm type of the 1st and 2nd kinds. The book focuses on methods and applications and this sets it apart from other works which have more focus on theory and analysis. The book is therefore accessible to a wide range of researchers and advanced students who will find it answers many of their practical problems of how to get started with a particular approach.
Iranian Journal of Mathematical Sciences and Informatics. Tue, Mar 16, [ Archive ]. Remember me Create Account Reset Password. Didgar M, Vahidi A. Didgar , A. Our proposed method is based upon utilizing the nth-order Taylor polynomial of unknown function at an arbitrary point and employing integration method to convert VFIEs into a system of linear equations with respect to unknown function and its derivatives. An approximate solution can be easily determined by solving the obtained system.
The collocation method for solving linear and nonlinear integral equations results in many integrals which must be evaluated numerically. In this paper, we give a general framework for discrete collocation methods , in which all integrals are replaced by numerical integrals. In some cases, the collocation method leads to solutions which are superconvergent at the collocation node points.
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Linear and Nonlinear Integral Equations: Methods and Applications is a Part I offers a comprehensive and systematic treatment of linear integral equations o. PDF · Introductory Concepts of Integral Equations. Abdul-Majid Wazwaz.
ReplyLinear and Nonlinear Integral Equations: Methods and Applications is a self-contained book divided into two parts. Part I offers a comprehensive and systematic.
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ReplyLinear and Nonlinear Integral Equations: Methods and Applications is de- Volterra integral equations and the linear Volterra integro-differential equa- tions, of.
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