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Cubic splines method for a system of third-order boundary value problems. (English) Zbl 1022.65082
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:
65L10Boundary value problems for ODE (numerical methods)
65L70Error bounds (numerical methods for ODE)
65L20Stability and convergence of numerical methods for ODE
34B05Linear boundary value problems for ODE
49J40Variational methods including variational inequalities
65K10Optimization techniques (numerical methods)