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Zbl 1022.65082
Al-Said, E.A.; Noor, M.A.
Cubic splines method for a system of third-order boundary value problems. (English)
[J] Appl. Math. Comput. 142, No.2-3, 195-204 (2003). ISSN 0096-3003

Summary: We use uniform cubic polynomial splines to develop a numerical method for computing approximations to the solution of a system of third-order boundary value problem associated with odd-order obstacle problems. Such problems arise in physical oceanography and can be studied in the framework of variational inequality theory. The convergence analysis of the new method is studied and an upper bound for the error is derived. A numerical example is given to illustrate the efficiency of the new method.

MSC 2000:: *65L10 Boundary value problems for ODE (numerical methods)
65L70 Error bounds (numerical methods for ODE)
65L20 Stability of numerical methods for ODE
34B05 Linear boundary value problems of ODE
49J40 Variational methods including variational inequalities
65K10 Optimization techniques (numerical methods)

Keywords: third-order boundary value problems; obstacle problems; variational; inequalities; cubic spline; finite difference; error bound; convergence; numerical example

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Zentralblatt MATH Berlin [Germany]