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Non-polynomial splines approach to the solution of sixth-order boundary-value problems. (English) Zbl 1130.65077
Summary: Non-polynomial splines, which are equivalent to seven-degree polynomial splines, are used to develop a class of numerical methods for computing approximations to the solution of sixth-order boundary-value problems with two-point boundary conditions. Second-, fourth- and sixth-order convergence is obtained by using standard procedures. It is shown that the present methods give approximations, which are better than those produced by other spline and domain decomposition methods. Numerical examples are given to illustrate the practical usefulness of the new approach.
MSC:
65L10Boundary value problems for ODE (numerical methods)
34B05Linear boundary value problems for ODE
65L20Stability and convergence of numerical methods for ODE