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International Journal of Computer Mathematics Volume 90, 2013 - Issue 9
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Section B

A new approach for numerical solution of integro-differential equations via Haar wavelets

Siraj-ul-Islam Department of Basic Sciences, University of Engineering and Technology, Peshawar, PakistanCorrespondence[email protected]
,
Imran Aziz Department of Basic Sciences, University of Engineering and Technology, Peshawar, Pakistan; Department of Mathematics, University of Peshawar, Peshawar, 25120, Pakistan
&
Muhammad Fayyaz Department of Basic Sciences, University of Engineering and Technology, Peshawar, Pakistan; Department of Computer Science, CECOS University Peshawar, Peshawar, 25120, Pakistan
Pages 1971-1989 | Received 26 Apr 2012, Accepted 21 Jan 2013, Published online: 25 Mar 2013

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A. H. Tedjani, A. Z. Amin, Abdel-Haleem Abdel-Aty, M. A. Abdelkawy & Mona Mahmoud. (2024) Legendre spectral collocation method for solving nonlinear fractional Fredholm integro-differential equations with convergence analysis. AIMS Mathematics 9:4, pages 7973-8000.
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Muhammad Ismail, Umer Saeed, Jehad Alzabut & Mujeeb ur Rehman. (2019) Approximate Solutions for Fractional Boundary Value Problems via Green-CAS Wavelet Method. Mathematics 7:12, pages 1164.
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Bijil Prakash, Amit Setia & Shourya Bose. (2017) Numerical Solution for a System of Fractional Differential Equations with Applications in Fluid Dynamics and Chemical Engineering. International Journal of Chemical Reactor Engineering 15:5.
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R. Chandra Guru Sekar, V. Balakumar & K. Murugesan. (2015) Method of Solving Linear System of Volterra Integro-Differential Equations Using the Single Term Walsh Series. International Journal of Applied and Computational Mathematics 3:2, pages 549-559.
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Sertan Alkan. (2017) Kesirli mertebeden integro-diferansiyel denklemlerin çözümü için sayısal bir yöntem. SAÜ Fen Bilimleri Enstitüsü Dergisi 21:2, pages 82-82.
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Imran Aziz & Siraj-ul-Islam. (2015) An Efficient Modified Haar Wavelet Collocation Method for Numerical Solution of Two-Dimensional Elliptic PDEs. Differential Equations and Dynamical Systems 25:2, pages 347-360.
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Sertan Alkan & Veysel Fuat Hatipoglu. (2017) Approximate solutions of Volterra-Fredholm integro-differential equations of fractional order. Tbilisi Mathematical Journal 10:2.
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S.Yu. Reutskiy. (2016) The backward substitution method for multipoint problems with linear Volterra–Fredholm integro-differential equations of the neutral type. Journal of Computational and Applied Mathematics 296, pages 724-738.
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Jian Chen, Yong Huang, Haiwu Rong, Tingting Wu & Taishan Zeng. (2015) A multiscale Galerkin method for second-order boundary value problems of Fredholm integro-differential equation. Journal of Computational and Applied Mathematics 290, pages 633-640.
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Santanu Saha Ray. 2015. Fractional Calculus with Applications for Nuclear Reactor Dynamics. Fractional Calculus with Applications for Nuclear Reactor Dynamics 130 159 .
Siraj-ul-Islam, Imran Aziz & Masood Ahmad. (2015) Numerical solution of two-dimensional elliptic PDEs with nonlocal boundary conditions. Computers & Mathematics with Applications 69:3, pages 180-205.
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Imran Aziz, Siraj-ul-Islam & Fawad Khan. (2014) A new method based on Haar wavelet for the numerical solution of two-dimensional nonlinear integral equations. Journal of Computational and Applied Mathematics 272, pages 70-80.
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S. Saha Ray & A. Patra. (2014) Numerical simulation for fractional order stationary neutron transport equation using Haar wavelet collocation method. Nuclear Engineering and Design 278, pages 71-85.
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A. Patra & S. Saha Ray. (2014) Two-dimensional Haar wavelet Collocation Method for the solution of Stationary Neutron Transport Equation in a homogeneous isotropic medium. Annals of Nuclear Energy 70, pages 30-35.
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Siraj-ul-Islam, Imran Aziz & A.S. Al-Fhaid. (2014) An improved method based on Haar wavelets for numerical solution of nonlinear integral and integro-differential equations of first and higher orders. Journal of Computational and Applied Mathematics 260, pages 449-469.
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Siraj-ul-Islam, Imran Aziz, A.S. Al-Fhaid & Ajmal Shah. (2013) A numerical assessment of parabolic partial differential equations using Haar and Legendre wavelets. Applied Mathematical Modelling 37:23, pages 9455-9481.
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S. H. Behiry. (2013) Numerical Solution of Nonlinear Fredholm Integrodifferential Equations by Hybrid of Block-Pulse Functions and Normalized Bernstein Polynomials. Abstract and Applied Analysis 2013, pages 1-8.
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