High order compact finite difference schemes for a system of third order boundary value problem. (English) Zbl 1308.65128
Summary: High order compact finite difference schemes are devised for general third order differential equations raised in the study of obstacle boundary value problems. These high order compact schemes are constructed by a modification, without additional workload in computation, of the second-order scheme developed in [M. A. Noor and E. A. Al-Said, J. Optim. Theory Appl. 112, No. 3, 627–637 (2002; Zbl 1002.49012)]. The convergence rates of these schemes are shown to be third- and fourth-order, respectively. Numerical experiments show that the proposed schemes are of high accuracy and are efficient.
MSC:
| 65L10 | Numerical solution of boundary value problems involving ordinary differential equations |
Keywords:
high order compact difference scheme; boundary value problem; third order obstacle problem; penalty function; convergence analysisCitations:
Zbl 1002.49012References:
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