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International Journal of Computer Mathematics Volume 45, 1992 - Issue 3-4
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Original Articles

Numerical methods for the solution of special sixth-order boundary-value problems

A. Boutayeb Department of Mathematics and Statistics, Brunel University, Uxbridge, Middlesex, UB8 3PH, England
&
E. H. Twizell Department of Mathematics and Statistics, Brunel University, Uxbridge, Middlesex, UB8 3PH, England
Pages 207-223 | Published online: 20 Mar 2007

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R. K. Mohanty, Geetan Manchanda, Arshad Khan & Gunjan Khurana. (2020) A new high accuracy method in exponential form based on off-step discretization for non-linear two point boundary value problems. Journal of Difference Equations and Applications 26:2, pages 171-202.
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Mohammed S. Mechee. (2019) Generalized RK integrators for solving class of sixth-order ordinary differential equations. Journal of Interdisciplinary Mathematics 22:8, pages 1457-1461.
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Abdelleh Lamnii, Hamid Mraoui, Driss Sbibih, Ahmed Tijini & Ahmed Zidna. (2008) Spline collocation method for solving linear sixth-order boundary-value problems. International Journal of Computer Mathematics 85:11, pages 1673-1684.
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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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Shahid S. Siddiqi & E. H. Twizell. (1998) Spline solutions of linear tenth-order boundary-value problems . International Journal of Computer Mathematics 68:3-4, pages 345-362.
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Shahid S. Siddiqi & E. H. Twizell. (1996) Spline solutions of linear sixth-order boundary-value problems. International Journal of Computer Mathematics 60:3-4, pages 295-304.
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A. Boutayeb & E. H. Twizell. (1993) Finite-difference methods for the solution of special eighth-order boundary-value problems. International Journal of Computer Mathematics 48:1-2, pages 63-75.
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H. M. Ahmed. (2023) Numerical Solutions of High-Order Differential Equations with Polynomial Coefficients Using a Bernstein Polynomial Basis. Mediterranean Journal of Mathematics 20:6.
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Akanksha Verma & Manoj Kumar. 2023. Advances in Mathematical Modelling, Applied Analysis and Computation. Advances in Mathematical Modelling, Applied Analysis and Computation 107 118 .
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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Aasma Khalid, Abdul Ghaffar, M. Nawaz Naeem, Kottakkaran Sooppy Nisar & Dumitru Baleanu. (2021) Solutions of BVPs arising in hydrodynamic and magnetohydro-dynamic stability theory using polynomial and non-polynomial splines. Alexandria Engineering Journal 60:1, pages 941-953.
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Amin Jajarmi & Dumitru Baleanu. (2020) A New Iterative Method for the Numerical Solution of High-Order Non-linear Fractional Boundary Value Problems. Frontiers in Physics 8.
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A. Khalid, M. N. Naeem, P. Agarwal, A. Ghaffar, Z. Ullah & S. Jain. (2019) Numerical approximation for the solution of linear sixth order boundary value problems by cubic B-spline. Advances in Difference Equations 2019:1.
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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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Dang Quang A & Dang Quang Long. (2018) A simple efficient method for solving sixth-order nonlinear boundary value problems. Computational and Applied Mathematics 37:S1, pages 16-26.
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Muhammad Sohaib, Sirajul Haq, Safyan Mukhtar & Imad Khan. (2018) Numerical solution of sixth-order boundary-value problems using Legendre wavelet collocation method. Results in Physics 8, pages 1204-1208.
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W. M. Abd-Elhameed & Y. H. Youssri. (2017) Spectral Solutions for Fifth-Order Boundary Value Problems Using Generalized Jacobi Operational Matrix of Derivatives. International Journal of Applied and Computational Mathematics 3:S1, pages 883-901.
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Ghazala Akram & Hira Tariq. (2015) An exponential spline technique for solving fractional boundary value problem. Calcolo 53:4, pages 545-558.
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Navnit Jha & Lesław K. Bieniasz. (2014) A Fifth (Six) Order Accurate, Three-Point Compact Finite Difference Scheme for the Numerical Solution of Sixth Order Boundary Value Problems on Geometric Meshes. Journal of Scientific Computing 64:3, pages 898-913.
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Feng-Gong Lang & Xiao-Ping Xu. (2015) An effective method for numerical solution and numerical derivatives for sixth order two-point boundary value problems. Computational Mathematics and Mathematical Physics 55:5, pages 811-822.
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SUQIN GE, WANYI WANG & QIUXIA YANG. (2014) DEPENDENCE OF EIGENVALUES OF SIXTH-ORDER BOUNDARY VALUE PROBLEMS ON THE BOUNDARY. Bulletin of the Australian Mathematical Society 90:3, pages 457-468.
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Majid Khan. (2014) An efficient analytical treatment of twelve order boundary value problems. Engineering Computations 31:1, pages 59-68.
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Inayat Ullah, Hamid Khan & M. T. Rahim. (2014) Numerical Solutions of Fifth and Sixth Order Nonlinear Boundary Value Problems by Daftardar Jafari Method. Journal of Computational Engineering 2014, pages 1-8.
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E.H. Doha, W.M. Abd-Elhameed & M.A. Bassuony. (2013) New algorithms for solving high even-order differential equations using third and fourth Chebyshev–Galerkin methods. Journal of Computational Physics 236, pages 563-579.
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Pooja Khandelwal & Talat Sultana. (2013) Parametric septic splines approach for the solution of linear sixth-order two-point boundary value problems. Applied Mathematics and Computation 219:12, pages 6856-6867.
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Mingzhu Li, Lijuan Chen & Qiang Ma. (2013) The Numerical Solution of Linear Sixth Order Boundary Value Problems with Quartic B-Splines. Journal of Applied Mathematics 2013, pages 1-7.
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Afgan Aslanov. (2012) A general formula for the series solution of high-order linear and nonlinear boundary value problems. Mathematical and Computer Modelling 55:3-4, pages 785-790.
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A. H. Bhrawy, A. S. Alofi & S. I. El-Soubhy. (2012) An Extension of the Legendre-Galerkin Method for Solving Sixth-Order Differential Equations with Variable Polynomial Coefficients. Mathematical Problems in Engineering 2012, pages 1-13.
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R. Jalilian & J. Rashidinia. (2010) Convergence analysis of nonic-spline solutions for special nonlinear sixth-order boundary value problems. Communications in Nonlinear Science and Numerical Simulation 15:12, pages 3805-3813.
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SYED TAUSEEF MOHYUD-DIN, MUHAMMAD ASLAM NOOR & KHALIDA INAYAT NOOR. (2011) VARIATIONAL ITERATION METHOD FOR SOLVING NONLINEAR HIGHER-ORDER INITIAL AND BOUNDARY VALUE PROBLEMS. International Journal of Computational Methods 06:04, pages 521-555.
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Syed Tauseef Mohyud-Din, Muhammad Aslam Noor & Asif Waheed. (2009) VARIATION OF PARAMETERS METHOD FOR SOLVING SIXTH-ORDER BOUNDARY VALUE PROBLEMS. Communications of the Korean Mathematical Society 24:4, pages 605-615.
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Muhammad Aslam Noor, Khalida Inayat Noor & Syed Tauseef Mohyud-Din. (2009) Variational iteration method for solving sixth-order boundary value problems. Communications in Nonlinear Science and Numerical Simulation 14:6, pages 2571-2580.
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Ben-Yu Guo, Jie Shen & Li-Lian Wang. (2009) Generalized Jacobi polynomials/functions and their applications. Applied Numerical Mathematics 59:5, pages 1011-1028.
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E.H. Doha, W.M. Abd-Elhameed & A.H. Bhrawy. (2009) Efficient spectral ultraspherical-Galerkin algorithms for the direct solution of 2nth-order linear differential equations. Applied Mathematical Modelling 33:4, pages 1982-1996.
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Muhammad Aslam Noor & Syed Tauseef Mohyud-Din. (2008) Homotopy perturbation method for solving sixth-order boundary value problems. Computers & Mathematics with Applications 55:12, pages 2953-2972.
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Shahid S. Siddiqi & Ghazala Akram. (2008) Septic spline solutions of sixth-order boundary value problems. Journal of Computational and Applied Mathematics 215:1, pages 288-301.
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M. A. Noor & S. T. Mohyud-Din. (2008) Homotopy Perturbation Method for Solving Nonlinear Higher-order Boundary Value Problems. International Journal of Nonlinear Sciences and Numerical Simulation 9:4.
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Siraj-ul-Islam, Ikram A. Tirmizi, Fazal-i-Haq & M. Azam Khan. (2008) Non-polynomial splines approach to the solution of sixth-order boundary-value problems. Applied Mathematics and Computation 195:1, pages 270-284.
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Shahid S. Siddiqi, Ghazala Akram & Saima Nazeer. (2007) Quintic spline solution of linear sixth-order boundary value problems. Applied Mathematics and Computation 189:1, pages 887-892.
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G.B. Loghmani & M. Ahmadinia. (2007) Numerical solution of sixth order boundary value problems with sixth degree B-spline functions. Applied Mathematics and Computation 186:2, pages 992-999.
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Ghazala Akram & Shahid S. Siddiqi. (2006) Solution of sixth order boundary value problems using non-polynomial spline technique. Applied Mathematics and Computation 181:1, pages 708-720.
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Y. Wang, Y.B. Zhao & G.W. Wei. (2003) A note on the numerical solution of high-order differential equations. Journal of Computational and Applied Mathematics 159:2, pages 387-398.
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Patricia J. Y. Wong & Ravi P. Agarwal. (2002) Characterization of eigenvalues for difference Equations subject to Lidstone conditions. Japan Journal of Industrial and Applied Mathematics 19:1, pages 1-18.
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Abdul-Majid Wazwaz. (2001) The numerical solution of sixth-order boundary value problems by the modified decomposition method. Applied Mathematics and Computation 118:2-3, pages 311-325.
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Patricia J.Y. Wong & Ravi P. Agarwal. (1999) Eigenvalues of Lidstone boundary value problems. Applied Mathematics and Computation 104:1, pages 15-31.
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Shahid S. Siddiqi & E.H. Twizell. (1997) Spline solutions of linear twelfth-order boundary-value problems. Journal of Computational and Applied Mathematics 78:2, pages 371-390.
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Shahid S. Siddiqi & E.H. Twizell. (1996) Spline solutions of linear eighth-order boundary-value problems. Computer Methods in Applied Mechanics and Engineering 131:3-4, pages 309-325.
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E. H. Twizell, A. Boutayeb & K. Djidjeli. (1994) Numerical methods for eighth-, tenth- and twelfth-order eigenvalue problems arising in thermal instability. Advances in Computational Mathematics 2:4, pages 407-436.
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