Finite-Difference Method for a System of Third-Order Boundary-Value Problems

In this paper, we develop a two-stage numerical method for computing the approximate solutions of third-order boundary-value problems associated with odd-order obstacle problems. We show that the present method is of order two. A numerical example is presented to illustrate the applicability of the new method. A comparison is also given with previously known results.

[1]  M. Noor.  New approximation schemes for general variational inequalities , 2000 .

[2]  J. Crank.  Free and moving boundary problems , 1984 .

[3]  Muhammad Aslam Noor,et al.  Numerical solutions of third-order obstacle problems , 1998, Int. J. Comput. Math..

[4]  E. O. Tuck,et al.  A Numerical and Asymptotic Study of Some Third-Order Ordinary Differential Equations Relevant to Draining and Coating Flows , 1990, SIAM Rev..

[5]  V. Filippov.  Variational Principles for Nonpotential Operators , 1989 .

[6]  Muhammed Aslam Noor,et al.  A numerical approach for odd-order obstacle problems , 1994 .

[7]  M. Noor.  General variational inequalities , 1988 .

[8]  Jack W. Macki,et al.  Case study from industry , 1995 .

[9]  F. Giannessi,et al.  Variational inequalities and network equilibrium problems , 1995 .

[10]  Hans Lewy,et al.  On the regularity of the solutions of the variational inequalities , 1969 .

[11]  M. Noor,et al.  Some aspects of variational inequalities , 1993 .

[12]  E. Al-Said,et al.  Finite difference scheme for variational inequalities , 1996 .

[13]  G. Mitra.  Variational Inequalities and Complementarity Problems — Theory and Application , 1980 .

[14]  G. Stampacchia,et al.  On the regularity of the solution of a variational inequality , 1969 .

[15]  V. M. Filippov,et al.  Variational principles for nonpotential operators , 1994 .

[16]  Carl-Erik Fröberg,et al.  Numerical mathematics - theory and computer applications , 1985 .

[17]  Steven R. Dunbar.  Geometric analysis of a nonlinear boundary value problem from physical oceanography , 1993 .

[18]  J. Boersma,et al.  Geometry of the Shoulder of a Packaging Machine , 1995, SIAM Rev..