On the use of splines for the numerical solution of nonlinear two-point boundary value problems
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Cubic splines on splines and quintic spline interpolations are used to approximate the derivative terms in a highly accurate scheme for the numerical solution of two-point boundary value problems. The storage requirement is essentially the same as for the usual trapezoidal rule but the local accuracy is improved fromO(h3) to eitherO(h6) orO(h7), whereh is the net size. The use of splines leads to solutions that reflect the smoothness of the slopes of the differential equations.
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- 1.F. B. Hildebrand,Introduction to Numerical Analysis, Second Ed., McGraw-Hill, New York (1974).Google Scholar
- 2.M. Lentini and V. Pereyra,A variable order finite difference method for nonlinear multipoint boundary value problems, Math. Comp. 28 (1974), pp. 981–1003.Google Scholar
- 3.H. B. Keller,Numerical solution of boundary value problems for ordinary differential equations: survey and some recent results of difference methods, inNumerical Solution of Boundary Value Problems for Ordinary Differential Equations, A. K. Aziz (Ed.), Academic Press, New York (1975), pp. 27–88.Google Scholar
- 4.J. H. Ahlberg, E. N. Wilson, and J. H. Walsh,The Theory of Splines and their Applications, Academic Press, New York (1967).Google Scholar
- 5.Z. Kopal,Numerical Analysis, Second Ed., John Wiley, New York (1961), pp. 555–557.Google Scholar
- 6.V. Dolezal and R. P. Tewarson,Error bounds for spline on spline computations, submitted for publication (1979).Google Scholar
- 8.R. P. Tewarson,Sparse Matrices, Academic Press, New York, (1973).Google Scholar
- 9.J. M. Ortega and W. C. Rheinboldt,Iterative Solution of Nonlinear Equations in Several Variables, Academic Press, New York (1970), p. 425.Google Scholar
- 10.M. Schultz,Spline Analysis, Prentice Hall (1973), p. 55.Google Scholar