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International Journal of Computer Mathematics Volume 60, 1996 - Issue 3-4
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Original Articles

Spline solutions of linear sixth-order boundary-value problems

Shahid S. Siddiqi Department of Mathematics and Statistics, Brunei University, Uxbridge, Middlesex, UB8 3PH, U.K
&
E. H. Twizell Department of Mathematics and Statistics, Brunei University, Uxbridge, Middlesex, UB8 3PH, U.K
Pages 295-304 | Published online: 19 Mar 2007

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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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M. A. Ramadan, I. F. Lashien & W. K. Zahra. (2008) A class of methods based on a septic non-polynomial spline function for the solution of sixth-order two-point boundary value problems. International Journal of Computer Mathematics 85:5, pages 759-770.
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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. (2002) The Numerical Solution of Special Fourth-Order Boundary Value Problems by the Modified Decomposition Method. International Journal of Computer Mathematics 79:3, pages 345-356.
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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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Pramod Kumar Pandey. (2018) Solving numerically a sixth order differential equation as coupled finite difference equations approach. Open Access Journal of Science 2:6.
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Iftikhar Ahmad, Fayyaz Ahmad, Muhammad Asif Zahoor Raja, Hira Ilyas, Nabeela Anwar & Zarqa Azad. (2016) Intelligent computing to solve fifth-order boundary value problem arising in induction motor models. Neural Computing and Applications 29:7, pages 449-466.
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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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Zakieh Avazzadeh & Mohammad Heydari. (2016) The application of block pulse functions for solving higher-order differential equations with multi-point boundary conditions. Advances in Difference Equations 2016:1.
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Navnit Jha, R. K. Mohanty & Vinod Chauhan. (2014) Efficient algorithms for fourth and sixth-order two-point non-linear boundary value problems using non-polynomial spline approximations on a geometric mesh. Computational and Applied Mathematics 35:2, pages 389-404.
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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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Navnit Jha, R. K. Mohanty & Vinod Chauhan. (2014) The Convergence of Geometric Mesh Cubic Spline Finite Difference Scheme for Nonlinear Higher Order Two-Point Boundary Value Problems. International Journal of Computational Mathematics 2014, pages 1-12.
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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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P. K. Pandey. (2013) Fourth order finite difference method for sixth order boundary value problems. Computational Mathematics and Mathematical Physics 53:1, pages 57-62.
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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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E. H. Doha & W. M. Abd-Elhameed. (2012) Efficient Solutions of Multidimensional Sixth-Order Boundary Value Problems Using Symmetric Generalized Jacobi-Galerkin Method. Abstract and Applied Analysis 2012, pages 1-19.
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Waleed Al-Hayani. (2011) Adomian decomposition method with Green’s function for sixth-order boundary value problems. Computers & Mathematics with Applications 61:6, pages 1567-1575.
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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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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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Huanmin Yao & Yingzhen Lin. (2009) Solving singular boundary-value problems of higher even-order. Journal of Computational and Applied Mathematics 223:2, pages 703-713.
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M.A. Ramadan, I.F. Lashien & W.K. Zahra. (2008) High order accuracy nonpolynomial spline solutions for 2μth order two point boundary value problems. Applied Mathematics and Computation 204:2, pages 920-927.
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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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Chi-Chang Wang, Zong-Yi Lee & Yiyo Kuo. (2008) Application of residual correction method in calculating upper and lower approximate solutions of fifth-order boundary-value problems. Applied Mathematics and Computation 199:2, pages 677-690.
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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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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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Hikmet Caglar & Nazan Caglar. (2007) Solution of fifth order boundary value problems by using local polynomial regression. Applied Mathematics and Computation 186:2, pages 952-956.
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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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Shahid S. Siddiqi & Ghazala Akram. (2006) Solution of fifth order boundary value problems using nonpolynomial spline technique. Applied Mathematics and Computation 175:2, pages 1574-1581.
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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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H.N. Çaglar, S.H. Çaglar & E.H. Twizell. (1999) The numerical solution of fifth-order boundary value problems with sixth-degree B-spline functions. Applied Mathematics Letters 12:5, pages 25-30.
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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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