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Solutions of tenth-order boundary value problems using eleventh degree spline. (English) Zbl 1119.65363
Summary: Numerical solutions of the tenth-order linear special case boundary value problems (BVPs) are obtained using eleventh degree spline. The end conditions consistent with the BVP, are also derived. S. S. Siddiqi and E. H. Twizell [Int. J. Comput. Math. 68, No. 3–4, 345–362 (1998; Zbl 0920.65049)] presented the solutions of tenth-order boundary value problems using tenth degree spline. Some unexpected results for the solution and higher order derivatives were obtained near the boundaries of the interval. No such unexpected situation is observed in this method, near the boundaries of the interval and the results are better in the whole interval. The algorithm developed approximates the solutions, and their higher order derivatives. Numerical illustrations are tabulated to compare the errors with those considered by Siddiqi and Twizell [loc. cit.] and the method is observed to be better.
MSC:
65L10Boundary value problems for ODE (numerical methods)
65L70Error bounds (numerical methods for ODE)
34B05Linear boundary value problems for ODE