Numerical solution of nonlinear Fredholm integral equations of the second kind using Haar wavelets
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TLDR
A computational method for solving nonlinear Fredholm integral equations of the second kind which is based on the use of Haar wavelets is presented, which shows efficiency of the method.About:
This article is published in Journal of Computational and Applied Mathematics.The article was published on 2009-03-01 and is currently open access. It has received 154 citations till now. The article focuses on the topics: Fredholm integral equation & Fredholm theory.read more
Citations
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Dissertation
Numerical solution of integrals and nonlinear integral equations by wavelets
Abdul Sathar,Mohammad Hasan +1 more
TL;DR: New methods based on Haar wavelets and linear Legendre multi-wavelets are proposed to solve problems arising in approximation of functions, integrals and integral equations to obtain numerical solutions of double, triple and N dimensional integrals.
Dissertation
Error Analyses for Nyström Methods for Solving Fredholm Integral and Integro-Differential Equations
TL;DR: In this article, the error bounds for FIEs and FIDEs are derived using Lagrange interpolation and Gaussian quadrature for the Volterra and Fredholm components respectively.
A numerical scheme for Fredholm integral equations
TL;DR: In this paper, a different numerical method for nonlinear Fredholm integral equations of the second kind with the continuous kernel with the main idea is to convert the integral equation problem into an optimization problem.
Proceedings ArticleDOI
Numerical solution by Haar wavelet collocation method for a class of higher order linear and nonlinear boundary value problems
TL;DR: In this paper, Haar wavelet collocation mechanism (HWCM) is developed for obtaining the solution of higher order linear and nonlinear boundary value problems (HOBVPs).
Journal ArticleDOI
Numerical Solution of Linear Volterra Integral Equation Systems of Second Kind by Radial Basis Functions
TL;DR: In this article , an approximation method for solving second kind Volterra integral equation systems by radial basis functions is proposed based on the minimization of a suitable functional in a discrete space generated by compactly supported radial basis function of Wendland type.
References
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Book
The Numerical Solution of Integral Equations of the Second Kind
TL;DR: In this paper, a brief discussion of integral equations is given, and the Nystrom method is used to solve multivariable integral equations on a piecewise smooth planar boundary.
Book
A mathematical introduction to wavelets
TL;DR: A mathematical introduction to the theory of orthogonal wavelets and their uses in analysing functions and function spaces, both in one and in several variables, can be found in this article.
Journal ArticleDOI
Haar wavelet method for solving lumped and distributed-parameter systems
C.F. Chen,C.H. Hsiao +1 more
TL;DR: In this article, an operational matrix of integration based on Haar wavelets is established, and a procedure for applying the matrix to analyse lumped and distributed-parameters dynamic systems is formulated.
Book
Piecewise Constant Orthogonal Functions and Their Application to Systems and Control
TL;DR: In this article, the authors proposed piecewise constant orthogonal basis functions (PCF) for linear and non-linear linear systems, and the optimal control of linear lag-free and time-lag systems.
Journal ArticleDOI
Numerical solution of linear Fredholm integral equation by using hybrid Taylor and Block-Pulse functions
TL;DR: A combination of Taylor and Block-Pulse functions on the interval [0,1], that is called Hybrid functions, is used to estimate the solution of a linear Fredholm integral equation of the second kind.
Related Papers (5)
Haar wavelet method for solving lumped and distributed-parameter systems
C.F. Chen,C.H. Hsiao +1 more