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International Journal of Computer Mathematics Volume 87, 2010 - Issue 6
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Section B

Numerical solution of fourth-order integro-differential equations using Chebyshev cardinal functions

Mehrdad Lakestani Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran
&
Mehdi Dehghan Department of Applied Mathematics, Faculty of Mathematics and Computer Sciences, Amirkabir University of Technology, Tehran, IranCorrespondence[email protected]
Pages 1389-1394 | Received 14 Mar 2008, Accepted 11 Jun 2008, Published online: 26 May 2009

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Robabeh Mohammadzadeh & Mehrdad Lakestani. (2015) Analysis of time-varying delay systems by hybrid of block-pulse functions and biorthogonal multiscaling functions. International Journal of Control 88:12, pages 2444-2456.
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Articles from other publishers (25)

Yan Wang, Jinxiang Wang & Xiaobin Yao. (2024) Monotone Iterative Technique for a Kind of Nonlinear Fourth-Order Integro-Differential Equations and Its Application. Advances in Mathematical Physics 2024, pages 1-10.
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Safar Irandoust‐Pakchin, Somaiyeh Abdi‐Mazraeh & Mohamed Adel. (2024) Application of flatlet oblique multiwavelets to solve the fractional stochastic integro‐differential equation using Galerkin method. Mathematical Methods in the Applied Sciences.
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Dang Quang Long & Dang Quang A. (2021) Existence results and numerical method for solving a fourth-order nonlinear integro-differential equation. Numerical Algorithms 90:2, pages 563-576.
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ŞUAYİP YÜZBAŞI YÜZBAŞIMEHMET SEZER. (2021) ON SOLUTIONS OF LINEAR FUNCTIONAL INTEGRAL AND INTEGRO-DIFFERENTIAL EQUATIONS VIA LAGRANGE POLYNOMIALS. Journal of Science and Arts 21:3, pages 707-720.
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M. Hosseininia, M. H. Heydari, M. R. Hooshmandasl, F. M. Maalek Ghaini & Z. Avazzadeh. (2020) A numerical method based on the Chebyshev cardinal functions for variable‐order fractional version of the fourth‐order 2D Kuramoto‐Sivashinsky equation. Mathematical Methods in the Applied Sciences 44:2, pages 1831-1842.
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Mohammad Hossein Heydari & Zakieh Avazzadeh. (2018) A computational method for solving two‐dimensional nonlinear variable‐order fractional optimal control problems. Asian Journal of Control 22:3, pages 1112-1126.
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M.H. Heydari. (2020) Chebyshev cardinal functions for a new class of nonlinear optimal control problems generated by Atangana–Baleanu–Caputo variable-order fractional derivative. Chaos, Solitons & Fractals 130, pages 109401.
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L. Saeedi, A. Tari & E. Babolian. (2019) Numerical Solution of Functional Volterra–Hammerstein Integro-differential Equations of Order Two. Iranian Journal of Science and Technology, Transactions A: Science 43:6, pages 2981-2992.
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M.H. Heydari & A. Atangana. (2019) A cardinal approach for nonlinear variable-order time fractional Schrödinger equation defined by Atangana–Baleanu–Caputo derivative. Chaos, Solitons & Fractals 128, pages 339-348.
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R. Roohi, M. H. Heydari & H. G. Sun. (2019) Numerical study of unsteady natural convection of variable-order fractional Jeffrey nanofluid over an oscillating plate in a porous medium involved with magnetic, chemical and heat absorption effects using Chebyshev cardinal functions. The European Physical Journal Plus 134:10.
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Mohammad Hossein Heydari, Zakieh Avazzadeh & Yin Yang. (2019) A computational method for solving variable-order fractional nonlinear diffusion-wave equation. Applied Mathematics and Computation 352, pages 235-248.
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Akbar Mohebbi. (2019) Crank–Nicolson and Legendre spectral collocation methods for a partial integro-differential equation with a singular kernel. Journal of Computational and Applied Mathematics 349, pages 197-206.
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Mohammad Hossein Heydari. (2018) A new direct method based on the Chebyshev cardinal functions for variable-order fractional optimal control problems. Journal of the Franklin Institute 355:12, pages 4970-4995.
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Farhad Fakhar-Izadi & Mehdi Dehghan. (2018) Fully spectral collocation method for nonlinear parabolic partial integro-differential equations. Applied Numerical Mathematics 123, pages 99-120.
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Safar Irandoust-Pakchin, Somayeh Abdi-Mazraeh & Ali Khani. (2018) Numerical Solution for a Variable-Order Fractional Nonlinear Cable Equation via Chebyshev Cardinal Functions. Computational Mathematics and Mathematical Physics 57:12, pages 2047-2056.
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E. Aruchunan, N. Khajohnsaksumeth & B. Wiwatanapataphee. (2016) A New Algorithm of Geometric Mean for Solving High-Order Fredholm Integro-differential Equations. A New Algorithm of Geometric Mean for Solving High-Order Fredholm Integro-differential Equations.
Esmail Babolian, Shahnam Javadi & Eslam Moradi. (2016) RKM for solving Bratu-type differential equations of fractional order. Mathematical Methods in the Applied Sciences 39:6, pages 1548-1557.
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Behzad Nemati Saray, Mehrdad Lakestani & Mohsen Razzaghi. (2015) Sparse representation of system of Fredholm integro-differential equations by using alpert multiwavelets. Computational Mathematics and Mathematical Physics 55:9, pages 1468-1483.
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Somayeh Abdi-mazraeh, Mehrdad Lakestani & Mehdi Dehghan. (2013) The construction of operational matrices of integral and fractional integral using the flatlet oblique multiwavelets. Journal of Vibration and Control 21:4, pages 818-832.
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M.M. Khader, N.H. Sweilam & W.Y. Kota. (2014) Cardinal functions for Legendre pseudo-spectral method for solving the integro-differential equations. Journal of the Egyptian Mathematical Society 22:3, pages 511-516.
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Xuehua Yang, Da Xu & Haixiang Zhang. (2013) Crank–Nicolson/quasi-wavelets method for solving fourth order partial integro-differential equation with a weakly singular kernel. Journal of Computational Physics 234, pages 317-329.
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N. H. Sweilam, M. M. Khader & W. Y. Kota. (2013) Numerical and Analytical Study for Fourth-Order Integro-Differential Equations Using a Pseudospectral Method. Mathematical Problems in Engineering 2013, pages 1-7.
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Amjad Alipanah & Mehdi Dehghan. (2011) A pseudospectral method for the solution of second-order integro-differential equations. Journal of Vibration and Control 17:14, pages 2158-2163.
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Mehrdad Lakestani, Mahmood Jokar & Mehdi Dehghan. (2011) Numerical solution of n th-order integro-differential equations using trigonometric wavelets . Mathematical Methods in the Applied Sciences 34:11, pages 1317-1329.
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Farhad Fakhar-Izadi & Mehdi Dehghan. (2011) The spectral methods for parabolic Volterra integro-differential equations. Journal of Computational and Applied Mathematics 235:14, pages 4032-4046.
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