Quartic spline collocation for second-order boundary value problems
نویسندگان
چکیده
Collocation methods based on quartic splines are presented for second-order two-point boundary value problems. In order to obtain a uniquely solvable linear system for the degrees of freedom of the quartic spline collocation approximation, in addition to the boundary conditions specified by the problem, extra boundary or near-boundary conditions are introduced. Non-optimal (fourth-order) and optimal (sixth-order) quartic-spline methods are considered. The theoretical behavior of the collocation methods is verified by numerical experiments. The extension of the methods to two-dimensional problems is briefly considered. Keywords— sixth order convergence, quartic splines, second-order BVP, collocation
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