Abstract
In this article some comments on the paper “parametric cubic spline approach to the solution of a system of second order boundary value problems” in (Khan and Aziz, J. Optim. Theory Appl. 118:45–54, 2003) are given. This paper concerns with a numerical method for solving a second order boundary value problem associated with obstacle, unilateral and contact problems. Corrections are given for the convergence analysis of the numerical method and the computational experiments.
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Khan, A., Aziz, T.: Parametric cubic spline approach to the solution of a system of second order boundary value problems. J. Optim. Theory Appl. 118, 45–54 (2003)
Henrici, P.: Discrete Variable Methods in Ordinary Differential Equations. Wiley, New York (1961)
Noor, M.A., Tirmizi, S.I.: Finite difference techniques for solving obstacle problems. Appl. Math. Lett. 1, 267–271 (1988)
Almualim, A.H.: Numerical methods for solving certain initial and boundary value problems in differential equations. M.Sc. Thesis, Mathematics Department, King Saud University (2009)
Noor, M.A., Khalifa, A.K.: Cubic spline collocation methods for unilateral problems. Int. J. Eng. Sci. 25, 1525–1530 (1987)
Al-Said, E.A., Noor, M.A., Al-Shejari, A.: Numerical solutions for system of second order boundary value problems. Korean J. Comput. Appl. Math. 5, 659–667 (1998)
Al-Said, E.A.: The use of cubic splines in the numerical solution of a system of second-order boundary value problems. Comput. Math. Appl. 42, 861–869 (2001)
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Communicated by D. Hull.
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Al-Said, E.A., Almualim, A.H. & Noor, M.A. On the Parametric Cubic Spline Approach for Solving Second Order Boundary Value Problems. J Optim Theory Appl 146, 810–812 (2010). https://doi.org/10.1007/s10957-010-9685-2
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DOI: https://doi.org/10.1007/s10957-010-9685-2