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Septic spline solutions of sixth-order boundary value problems. (English) Zbl 1138.65062

Summary: A septic spline is used for the numerical solution of the sixth-order linear, special case boundary value problem. End conditions for the definition of the septic spline are derived, consistent with the sixth-order boundary value problem. The algorithm developed approximates the solution and their higher-order derivatives. The method is also proved to be second-order convergent.

Three examples are considered for the numerical illustrations of the method developed. The method developed in this paper is also compared with that developed by M. El-Gamel, J. R. Cannon, J. Latour, and A. I. Zayed, [Math. Comput. 73, No. 247, 1325–1343 (2003; Zbl 1054.65085)], as well and is observed to be better.

65L10Boundary value problems for ODE (numerical methods)
34B05Linear boundary value problems for ODE
65L20Stability and convergence of numerical methods for ODE