Nonpolynomial sextic spline method for the solution along with convergence of linear special case fifth-order two-point boundary value problems.

*(English)*Zbl 1125.65072The authors investigate the nonpolynomial sextic spline method for the solution along with convergence of linear special case fifth-order two-point boundary value problems. Using the continuity of the derivatives at the knots, the consistency relations in terms of values of the spline and its fifth derivatives at the knots along with consistent end conditions are determined. The nonpolynomial sextic spline solution approximating the analytic solution of the boundary value problem is discussed. An error bound of the solution is given. Examples are given to illustrate the methods discussed.

Reviewer: Seenith Sivasundaram (Daytona Beach)

##### MSC:

65L10 | Numerical solution of boundary value problems involving ordinary differential equations |

34B05 | Linear boundary value problems for ordinary differential equations |

65L20 | Stability and convergence of numerical methods for ordinary differential equations |

##### Keywords:

nonpolynomial sextic spline; convergence; difference equations; end conditions; numerical examples; fifth-order two-point boundary value problems
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\textit{S. S. Siddiqi} et al., Appl. Math. Comput. 190, No. 1, 532--541 (2007; Zbl 1125.65072)

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##### References:

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