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International Journal of Computer Mathematics Volume 40, 1991 - Issue 1-2
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Original Articles

A note on solving the fourth order parabolic equation by the age method

D.J. Evans Parallel Algorithms Research Centre, Loughborough University, Loughborough, LEU 3TU, Leicestershire
&
W.S. Yousif Parallel Algorithms Research Centre, Loughborough University, Loughborough, LEU 3TU, Leicestershire
Pages 93-97 | Received 30 Sep 1990, Published online: 20 Mar 2007

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J. Rashidinia & R. Mohammadi. (2010) Sextic spline solution of variable coefficient fourth-order parabolic equations. International Journal of Computer Mathematics 87:15, pages 3443-3454.
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J. Rashidinia & R. Mohammadi. (2009) Numerical Methods Based on Non-Polynomial Sextic Spline for Solution of Variable Coefficient Fourth-Order Wave Equations. International Journal for Computational Methods in Engineering Science and Mechanics 10:4, pages 266-276.
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Arshad Khan, Islam Khan & Tariq Aziz. (2005) Sextic spline solution for solving a fourth-order parabolic partial differential equation. International Journal of Computer Mathematics 82:7, pages 871-879.
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R. K. Mohanty, D. J. Evans & Dinesh Kumar. (2003) High Accuracy Difference Formulae For A Fourth Order Quasi-Linear Parabolic Initial Boundary Value Problem Of First Kind. International Journal of Computer Mathematics 80:3, pages 381-398.
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A.-M. Wazwaz. (1995) On the solution of the fourth order parabolic equation by the decomposition method. International Journal of Computer Mathematics 57:3-4, pages 213-217.
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D.J. Evans & W.S. Yousif. (1993) The numerical solution of 2-dimensional fourth order partial differential equations by the age fractional method. International Journal of Computer Mathematics 49:1-2, pages 67-74.
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Mohamed Moustafa, Youssri Hassan Youssri & Ahmed Gamal Atta. (2023) Explicit Chebyshev Petrov–Galerkin scheme for time-fractional fourth-order uniform Euler–Bernoulli pinned–pinned beam equation. Nonlinear Engineering 12:1.
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Meshari Alesemi. (2023) Numerical Analysis of Fractional-Order Parabolic Equation Involving Atangana–Baleanu Derivative. Symmetry 15:1, pages 237.
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Seda Çayan, B. Burak Özhan & Mehmet Sezer. (2022) Collocation approaches to the mathematical model of an Euler–Bernoulli beam vibrations. Mathematics and Computers in Simulation 197, pages 32-44.
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Muhammad Naeem, Omar Fouad Azhar, Ahmed M. Zidan, Kamsing Nonlaopon & Rasool Shah. (2021) Numerical Analysis of Fractional-Order Parabolic Equations via Elzaki Transform. Journal of Function Spaces 2021, pages 1-10.
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Ravi P. Agarwal, Fatemah Mofarreh, Rasool Shah, Waewta Luangboon & Kamsing Nonlaopon. (2021) An Analytical Technique, Based on Natural Transform to Solve Fractional-Order Parabolic Equations. Entropy 23:8, pages 1086.
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Ömer ORUÇ, Alaattin ESEN & Fatih BULUT. (2021) Numerical investigation of dynamic Euler-Bernoulli equation via 3-Scale Haar wavelet collocation method. Hacettepe Journal of Mathematics and Statistics 50:1, pages 159-179.
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Dessalegn Mekonnen Yadeta, Ademe Kebede Gizaw & Yesuf Obsie Mussa. (2020) Approximate Analytical Solution of One-Dimensional Beam Equations by Using Time-Fractional Reduced Differential Transform Method. Journal of Applied Mathematics 2020, pages 1-13.
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Muhammad Nadeem, Fengquan Li & Hijaz Ahmad. (2019) Modified Laplace variational iteration method for solving fourth-order parabolic partial differential equation with variable coefficients. Computers & Mathematics with Applications 78:6, pages 2052-2062.
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Maohua Ran, Taibai Luo & Li Zhang. (2019) Unconditionally stable compact theta schemes for solving the linear and semi-linear fourth-order diffusion equations. Applied Mathematics and Computation 342, pages 118-129.
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Talat Sultana & Pooja Khandelwal. (2018) Tension spline technique for the solution of fourth-order parabolic partial differential equation. Malaya Journal of Matematik 06:03, pages 514-520.
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R.K. Mohanty, Sean McKee & Deepti Kaur. (2017) A class of two-level implicit unconditionally stable methods for a fourth order parabolic equation. Applied Mathematics and Computation 309, pages 272-280.
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Ranjan Kumar Mohanty & Deepti Kaur. (2016) A class of quasi-variable mesh methods based on off-step discretization for the numerical solution of fourth-order quasi-linear parabolic partial differential equations. Advances in Difference Equations 2016:1.
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R.K. Mohanty & Deepti Kaur. (2016) High accuracy implicit variable mesh methods for numerical study of special types of fourth order non-linear parabolic equations. Applied Mathematics and Computation 273, pages 678-696.
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Mohamed El-Gamel. (2014) A note on solving the fourth-order parabolic equation by the sinc-Galerkin method. Calcolo 52:3, pages 327-342.
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Reza Mohammadi. (2014) Sextic B-spline collocation method for solving Euler–Bernoulli Beam Models. Applied Mathematics and Computation 241, pages 151-166.
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V.G. Gupta & Sumit Gupta. (2013) ANALYTICAL SOLUTION OF SINGULAR FOURTH ORDER PARABOLIC PARTIAL DIFFERENTIAL EQUATIONS OF VARIABLE COEFFICIENTS BY USING HOMOTOPY PERTURBATION TRANSFORM METHOD. Journal of applied mathematics & informatics 31:1_2, pages 165-177.
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Liyun Su, Tianshun Yan, Yanyong Zhao & Fenglan Li. (2012) Local Polynomial Regression Solution for Partial Differential Equations with Initial and Boundary Values. Discrete Dynamics in Nature and Society 2012, pages 1-11.
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Muhammad Aslam Noor, Khalida Inayat Noor & Syed Tauseef Mohyud-Din. (2009) Modified variational iteration technique for solving singular fourth-order parabolic partial differential equations. Nonlinear Analysis: Theory, Methods & Applications 71:12, pages e630-e640.
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J. Sulaiman, M. K. Hasan, M. Othman & Z. Yaacob. (2009) Quarter-Sweep Arithmetic Mean iterative algorithm to solve fourth-order parabolic equations. Quarter-Sweep Arithmetic Mean iterative algorithm to solve fourth-order parabolic equations.
Arshad Khan. (2008) Non‐polynomials spline methods for solving a fourth‐order parabolic equation. PAMM 7:1, pages 2020133-2020134.
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Tariq Aziz, Arshad Khan & Jalil Rashidinia. (2005) Spline methods for the solution of fourth-order parabolic partial differential equations. Applied Mathematics and Computation 167:1, pages 153-166.
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Abdul-Majid Wazwaz. (2002) Exact solutions for variable coefficients fourth-order parabolic partial differential equations in higher-dimensional spaces. Applied Mathematics and Computation 130:2-3, pages 415-424.
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Abdul-Majid Wazwaz. (2001) Analytic treatment for variable coefficient fourth-order parabolic partial differential equations. Applied Mathematics and Computation 123:2, pages 219-227.
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