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Original Articles

The Numerical Solution of Special Fourth-Order Boundary Value Problems by the Modified Decomposition Method

Pages 345-356 | Published online: 15 Sep 2010

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Mohamed Ali Hajji & Kamel Al-Khaled. (2008) Numerical methods for nonlinear fourth-order boundary value problems with applications. International Journal of Computer Mathematics 85:1, pages 83-104.
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A. Boutayeb & A. Chetouani. (2007) A mini-review of numerical methods for high-order problems† . International Journal of Computer Mathematics 84:4, pages 563-579.
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Abdul-Majid Wazwaz. (2005) The modified decomposition method for analytic treatment of non-linear integral equations and systems of non-linear integral equations. International Journal of Computer Mathematics 82:9, pages 1107-1115.
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Yunlei Yang, Yang Wu, Muzhou Hou, Jianshu Luo & Xiaoliang Xie. (2023) Solving Emden–Fowler Equations Using Improved Extreme Learning Machine Algorithm Based on Block Legendre Basis Neural Network. Neural Processing Letters 55:6, pages 7135-7154.
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Merve YÜCEL, Fahreddin MUHTAROV & Oktay MUKHTAROV. (2022) A New Transformation Method for Solving High-Order Boundary Value Problems. Journal of New Theory:40, pages 90-100.
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Mohamed El-Gamel, Nesreen Mohamed & Waleed Adel. (2022) Numerical Study of a Nonlinear High Order Boundary Value Problems Using Genocchi Collocation Technique. International Journal of Applied and Computational Mathematics 8:3.
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Prakash Kumar Das. (2021) The genesis of two-hump, W-shaped and M-shaped soliton propagations of the coupled Schrödinger–Boussinesq equations with conformable derivative. Optical and Quantum Electronics 53:6.
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Saurabh Tomar. (2020) A Computationally Efficient Iterative Scheme for Solving Fourth-Order Boundary Value Problems. International Journal of Applied and Computational Mathematics 6:4.
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A. Karimi Dizicheh, S. Salahshour, A. Ahmadian & D. Baleanu. (2020) A novel algorithm based on the Legendre wavelets spectral technique for solving the Lane–Emden equations. Applied Numerical Mathematics 153, pages 443-456.
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Sucheta Nayak & Arshad Khan. (2020) Variable Mesh Polynomial Spline Discretization for Solving Higher Order Nonlinear Singular Boundary Value Problems. Differential Equations and Dynamical Systems 28:3, pages 617-631.
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Hunter Johnston, Carl Leake & Daniele Mortari. (2020) Least-Squares Solutions of Eighth-Order Boundary Value Problems Using the Theory of Functional Connections. Mathematics 8:3, pages 397.
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Shahna & Arshad Khan. (2019) Approximations for higher order boundary value problems using non-polynomial quadratic spline based on off-step points. Journal of King Saud University - Science 31:4, pages 737-745.
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Ali Akgül & Esra Karatas Akgül. (2019) A Novel Method for Solutions of Fourth-Order Fractional Boundary Value Problems. Fractal and Fractional 3:2, pages 33.
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Nauman Khalid, Muhammad Abbas & Muhammad Kashif Iqbal. (2019) Non-polynomial quintic spline for solving fourth-order fractional boundary value problems involving product terms. Applied Mathematics and Computation 349, pages 393-407.
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Onyejekwe Okey Oseloka. (2018) Integral formulations for 1-D Biharmonic and Second Order Coupled Linear and Nonlinear Boundary Value Problems. Annals of Mathematics and Physics, pages 001-004.
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Ranjan Kumar Mohanty, Sucheta Nayak & Arshad Khan. (2017) Non-polynomial cubic spline discretization for system of non-linear singular boundary value problems using variable mesh. Advances in Difference Equations 2017:1.
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Waleed M Abd-Elhameed, Hany M Ahmed & Youssri H Youssri. (2016) A new generalized Jacobi Galerkin operational matrix of derivatives: two algorithms for solving fourth-order boundary value problems. Advances in Difference Equations 2016:1.
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Mahmoud Behroozifar. (2015) Spectral method for solving high order nonlinear boundary value problems via operational matrices. BIT Numerical Mathematics 55:4, pages 901-925.
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Prakash Kumar Das & M. M. Panja. 2015. Applied Mathematics. Applied Mathematics 193 201 .
Yin-shan Yun, Temuer Chaolu & Jun-sheng Duan. (2014) A segmented and weighted Adomian decomposition algorithm for boundary value problem of nonlinear groundwater equation. Mathematical Methods in the Applied Sciences 37:16, pages 2406-2418.
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Randhir Singh, Jitendra Kumar & Gnaneshwar Nelakanti. (2014) Approximate series solution of fourth-order boundary value problems using decomposition method with Green’s function. Journal of Mathematical Chemistry 52:4, pages 1099-1118.
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Ayesha Sohail, Khadija Maqbool & Tasawar Hayat. (2014) Painlevé property and approximate solutions using Adomian decomposition for a nonlinear KdV-like wave equation. Applied Mathematics and Computation 229, pages 359-366.
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Jun-Sheng Duan, Randolph Rach, Abdul-Majid Wazwaz, Temuer Chaolu & Zhong Wang. (2013) A new modified Adomian decomposition method and its multistage form for solving nonlinear boundary value problems with Robin boundary conditions. Applied Mathematical Modelling 37:20-21, pages 8687-8708.
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Ali Mohamadnejad Rismani & Hossein Monfared. (2012) Numerical solution of singular IVPs of Lane–Emden type using a modified Legendre-spectral method. Applied Mathematical Modelling 36:10, pages 4830-4836.
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Feyed Ben Zitoun & Yves Cherruault. (2012) A method for solving nonlinear integro‐differential equations. Kybernetes 41:1/2, pages 35-50.
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Jun-Sheng Duan & Randolph Rach. (2011) A new modification of the Adomian decomposition method for solving boundary value problems for higher order nonlinear differential equations. Applied Mathematics and Computation 218:8, pages 4090-4118.
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M.A. Hajji. (2011) A numerical scheme for multi-point special boundary-value problems and application to fluid flow through porous layers. Applied Mathematics and Computation 217:12, pages 5632-5642.
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Feyed Ben Zitoun & Yves Cherruault. (2010) A method for solving nonlinear differential equations. Kybernetes 39:4, pages 578-597.
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S. Asghar, M. Mushtaq & T. Hayat. (2010) Flow in a slowly deforming channel with weak permeability: An analytical approach. Nonlinear Analysis: Real World Applications 11:1, pages 555-561.
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Xufeng Shang, Peng Wu & Xingping Shao. (2009) An efficient method for solving Emden–Fowler equations. Journal of the Franklin Institute 346:9, pages 889-897.
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Fazhan Geng. (2009) A new reproducing kernel Hilbert space method for solving nonlinear fourth-order boundary value problems. Applied Mathematics and Computation 213:1, pages 163-169.
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Feyed Ben Zitoun & Yves Cherruault. (2009) A new algorithm for solving nonlinear boundary value problems. Kybernetes 38:5, pages 681-697.
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Zhou Yu-Bin & Li Chao. (2009) Application of Modified G ′/ G -Expansion Method to Traveling Wave Solutions for Whitham–Broer–Kaup-Like Equations . Communications in Theoretical Physics 51:4, pages 664-670.
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T. Hayat, Q. Hussain & T. Javed. (2009) The modified decomposition method and Padé approximants for the MHD flow over a non-linear stretching sheet. Nonlinear Analysis: Real World Applications 10:2, pages 966-973.
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A. Sami Bataineh, M.S.M. Noorani & I. Hashim. (2009) Homotopy analysis method for singular IVPs of Emden–Fowler type. Communications in Nonlinear Science and Numerical Simulation 14:4, pages 1121-1131.
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M.S.H. Chowdhury & I. Hashim. (2009) Solutions of Emden–Fowler equations by homotopy-perturbation method. Nonlinear Analysis: Real World Applications 10:1, pages 104-115.
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S. A. El-Wakil & M. A. Abdou. (2007) New applications of variational iteration method using Adomian polynomials. Nonlinear Dynamics 52:1-2, pages 41-49.
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Shaher Momani & Muhammad Aslam Noor. (2007) Numerical comparison of methods for solving a special fourth-order boundary value problem. Applied Mathematics and Computation 191:1, pages 218-224.
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Vedat Suat Ertürk & Shaher Momani. (2007) Comparing numerical methods for solving fourth-order boundary value problems. Applied Mathematics and Computation 188:2, pages 1963-1968.
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Kamel Al-Khaled & M. Naim Anwar. (2007) Numerical comparison of methods for solving second-order ordinary initial value problems. Applied Mathematical Modelling 31:2, pages 292-301.
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Abdul-Majid Wazwaz. (2006) A comparison study between the modified decomposition method and the traditional methods for solving nonlinear integral equations. Applied Mathematics and Computation 181:2, pages 1703-1712.
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Shaher Momani & Khaled Moadi. (2006) A reliable algorithm for solving fourth-order boundary value problems. Journal of Applied Mathematics and Computing 22:3, pages 185-197.
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I. Hashim, M.S.M. Noorani, R. Ahmad, S.A. Bakar, E.S. Ismail & A.M. Zakaria. (2006) Accuracy of the Adomian decomposition method applied to the Lorenz system. Chaos, Solitons & Fractals 28:5, pages 1149-1158.
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Abdul-Majid Wazwaz. (2006) The modified decomposition method and Padé approximants for a boundary layer equation in unbounded domain. Applied Mathematics and Computation 177:2, pages 737-744.
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Abdul-Majid Wazwaz. (2006) The modified decomposition method for analytic treatment of differential equations. Applied Mathematics and Computation 173:1, pages 165-176.
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Xing-Guo Luo. (2005) A two-step Adomian decomposition method. Applied Mathematics and Computation 170:1, pages 570-583.
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M.A. Abdou. (2005) Adomian decomposition method for solving the telegraph equation in charged particle transport. Journal of Quantitative Spectroscopy and Radiative Transfer 95:3, pages 407-414.
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