New algorithms for the numerical solution of nonlinear Fredholm and Volterra integral equations using Haar wavelets
Imran Aziz,Siraj-ul-Islam +1 more
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TLDR
The advantage of the proposed new algorithms based on Haar wavelets is that it does not involve any intermediate numerical technique for evaluation of the integral present in integral equations.About:
This article is published in Journal of Computational and Applied Mathematics.The article was published on 2013-02-01 and is currently open access. It has received 117 citations till now. The article focuses on the topics: Volterra integral equation & Nyström method.read more
Citations
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Convergence theorem for the Haar wavelet based discretization method
TL;DR: In this paper, the accuracy issues of Haar wavelet method are studied and the order of convergence as well as error bound of the Haar Wavelet method is derived for general nth order ODE.
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A new method based on Haar wavelet for the numerical solution of two-dimensional nonlinear integral equations
TL;DR: A new numerical method based on Haar wavelet for two-dimensional nonlinear Fredholm, Volterra and VolterRA-Fredholm integral equations of first and second kind which does not involve numerical integration which results in an improved accuracy of the method.
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Numerical solution of a class of delay differential and delay partial differential equations via Haar wavelet
Imran Aziz,Rohul Amin +1 more
TL;DR: The numerical results show that the Haar wavelet collocation method is simply applicable, accurate, efficient and robust.
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On the accuracy of the Haar wavelet discretization method
TL;DR: In this article, the authors used Haar wavelet discretization method (HWDM) for FG beams and its accuracy estimates for the convergence analysis is performed for differential equations covering a wide class of composite and nanostructures.
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An improved method based on Haar wavelets for numerical solution of nonlinear integral and integro-differential equations of first and higher orders
TL;DR: The present approach is an improved form of the Haar wavelet methods, and is easily extendable to higher order IDEs of higher orders with initial- and boundary-conditions.
References
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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.
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Numerical solution of evolution equations by the Haar wavelet method
TL;DR: An efficient numerical method for solution of nonlinear evolution equations based on the Haar wavelets approach is proposed and tested in the case of Burgers and sine-Gordon equations, demonstrating that the accuracy of theHaar wavelet solutions is quite high even in the cases of a small number of grid points.
Journal ArticleDOI
Legendre wavelets method for the nonlinear Volterra-Fredholm integral equations
TL;DR: A numerical method for solving the nonlinear Volterra-Fredholm integral equations is presented, based upon Legendre wavelet approximations and the Gaussian integration method.
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Numerical solution of differential equations by using Chebyshev wavelet operational matrix of integration
Esmail Babolian,F. Fattahzadeh +1 more
TL;DR: Comparison examples are included to demonstrate the superiority of operational matrix of Chebyshev wavelets to those of Legendre wavelets.
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The numerical solution of second-order boundary-value problems by collocation method with the Haar wavelets
TL;DR: An efficient numerical method based on uniform Haar wavelets for the numerical solution of second-order boundary-value problems (BVPs) arising in the mathematical modeling of deformation of beams and plate deflection theory, deflection of a cantilever beam under a concentrated load, obstacle problems and many other engineering applications.
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Haar wavelet method for solving lumped and distributed-parameter systems
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