Quartic non-polynomial spline functions are used to develop numerical methods for
computing approximations to the solution of systems of second-order boundary-value
problems associated with obstacle, unilateral, and contact problems. It is shown
that the present methods give approximations, which are better than those produced
by other collocation, finite-difference and spline methods. Convergence analysis of
the method for obstacle problems is discussed. Numeric example’s given to
illustrate practical usefulness of the new approach.
Al-Said, E. A.
(1996).
Spline solutions for system of second-order boundary-value problems
. Int. J. Comput. Math., 62:
143-154
.
2.
Al-Said, E. A.
(1998).
Cubic spline method for solving two point boundary value problems
. Korean J. Comput. Appl. Math., 5:
669-680
3.
Al-Said, E. A.
(1999a).
Spline methods for solving system of second-order boundary-value problems
. Int. J. Comput. Math., 70:
717-727
.
4.
Al-Said, E. A.
(1999b).
Smooth spline solutions for a system of second order boundary value problems
. J. Nat. Geomet., 16:
18-27
.
5.
Al-Said, E. A.
(2001).
The use of cubic splines in the numerical solution of a system of
second-order boundary value problems
. Comput. Math. Applics., 42:
861-869
.
6.
Al-Said, E. A.
and
Noor, M. A.
(2001).
Modified Numerov method for solving system of second-order boundary-value problems
. Korean J. Comput. Appl. Math., 8:
129-136
.
7.
Al-Said, E. A.
(2005).
Quartic splines solutions for a system of second order boundary value problems
. Applied Mathematics and Computation, 166:
254-264
8.
Baiocchi, C.
and
Capelo, A.
(1984). Variational and Quasi-Variational Inequalities,
New York: John Wiley and Sons
.
9.
Cottle, R. W.
,
Giannessi, F.
and
Lions, J. L.
(1984). Variational Inequalities and Complementarity
Problems: Theory and Applications,
New York: Wiley and Sons
.
10.
Lewy, H.
and
Stampacchia, G.
(1969).
On the regularity of the solution of the variational inequalities
. Comm. Pure Appl. Math., 22:
153-188
.
11.
Lions, J. L.
and
Stampacchia, G.
(1967).
Variational inequalities
. Comm. Pure Appl. Math., 20:
493-519
.
12.
Noor, M. A.
and
Khalifa, A. K.
(1987).
Cubic splines collocation methods for unilateral problems
. Int. J. Eng. Sci., 25:
1527-1530
.
13.
Siraj-ul-Islam, Khan, M. A.
,
Tirmizi, S. I. A.
and
Twizell, E. H.
(2005).
A non-polynomial spline approach to the solution of a system of third-order
boundary-value problems using non-polynomial splines
. Appl. Math. Computation, 168(1):
152-163
.
14.
Usmani, R. A.
(1992).
The use of quartic spline in the numerical solution of fourth-order
boundary-value problem
. J. Computational Appl. Math., 44:
187-199
.
15.
Villaggio, F.
(1981).
The Ritz method in solving unilateral problems in elasticity
. Meccanica, 16(3):
123-127
.
