Numerical solution of a system of fourth order boundary value problems using cubic non-polynomial spline method

Applied Mathematics and Computation

Volumn 190, Issue 1, 2007, Pages 652-661

  Siddiqi, Shahid S ^a   Akram, Ghazala ^a  

^a UNIVERSITY OF THE PUNJAB   (Pakistan)

Author keywords

Non polynomial spline; Obstacle problems; System of boundary value problems; Variational inequalities

Indexed keywords

BOUNDARY CONDITIONS; COMPUTATIONAL EFFICIENCY; FINITE DIFFERENCE METHOD; PROBLEM SOLVING; VARIATIONAL TECHNIQUES;

NON-POLYNOMIAL SPLINE; OBSTACLE PROBLEMS; VARIATIONAL INEQUALITIES;

BOUNDARY VALUE PROBLEMS;

EID: 34249868482     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2007.01.074     Document Type: Article

References (21)

1. Khan A., Noor M.A., and Aziz T. Parametric quintic-spline approach to the solution of a system of fourth-order boundary-value problems. Journal of Optimization Theory and Applications 122 2 (2004) 309-322
2. Al-Said E.A., and Noor M.A. Computational methods for fourth-order obstacle boundary-value problems. Communications in Applied Nonlinear Analysis 2 (1995) 73-83
3. Al-Said E.A. Spline methods for solving system of second-order boundary-value problems. International Journal of Computational Mathematics 70 (1999) 717-727
4. Al-Said E.A. The use of cubic splines in the numerical solution of a system of second-order boundary value problems. Computers and Mathematics with Applications 42 (2001) 861-869
5. Twizell E.H., and Tirmizi S.I.A. A sixth-order multiderivative method for two beam problems. International Journal for Numerical Methods in Engineering 23 (1986) 2089-2102
6. Gao F., and Chi C.-M. Solving third-order obstacle problems with quartic B-splines. Applied Mathematics and Computation 180 (2006) 270-274
7. Akram G., and Siddiqi S.S. Solution of sixth order boundary value problems using non-polynomial spline technique. Applied Mathematics and Computation 181 (2006) 708-720
8. Lewy H., and Stampacchia G. On the regularity of the solution of the variational inequalities. Communications in Pure and Applied Mathematics 22 (1969) 153-188
9. Crank J. Free and moving boundary-value problems (1984), Clarendon Press, Oxford, UK
10. Noor M.A., and Tirmizi S.I.A. Highly accurate methods for solving unilateral problems. Punjab University Journal of Mathematics 22 (1989-90) 19-30
11. Van Daele M., Vanden Berghe G., and De Meyer H. A smooth approximation for the solution of a fourth-order boundary value problem based on nonpolynomial splines. Journal of Computational and Applied Mathematics 51 3 (1994) 383-394
12. Kikuchi N., and Oden T.J. Contact Problems in Elasticity (1988), SIAM, Philadelphia, Pennsylvania
13. Papamichael N., and Worsey A.J. A cubic spline method for the solution of a linear fourth-order two-point boundary value problem. Journal of Comptutation and Applied Mathematics 7 (1981) 187-189
14. Glowinski R., Lions J.L., and Tremolieres R. Numerical Analysis of Variational Inequalities (1981), North-Holland, Amsterdam, Holland
15. Usmani R.A. Discrete variable methods for a boundary value problem with engineering applications. Mathematics of Computation 32 144 (1978) 1087-1096
16. Usmani R.A. Discrete methods for boundary value problems with applications in plate deflection theory. ZAMP 30 (1979) 87-99
17. Siddiqi S.S., and Akram G. Solution of fifth-order boundary-value problems using non polynomial spline technique. Applied Mathematics and Computation 175 2 (2006) 1574-1581
18. Shahid S. Siddiqi, Ghazala Akram, Solution of eighth-order boundary-value problems using non polynomial spline technique, International Journal of Computer Mathematics, submitted for publication.
19. Siddiqi S.S., and Akram G. Solution of the system of fourth-order boundary-value problems using non polynomial spline technique. Applied Mathematics and Computation 185 (2007) 128-135
20. Siraj-ul-Islam, Khan M.A., Tirmizi I.A., and Twizell E.H. Non polynomial spline approach to the solution of a system of third-order boundary-value problems. Applied Mathematics and Computation 168 1 (2005) 152-163
21. Lucas T.R. Error bounds for interpolating cubic splines under various end conditions. SIAM Journal of Numerical Analysis 11 3 (1974) 569-584