Part II Numerical Mathematics

BIT Numerical Mathematics

, Volume 20, Issue 2, pp 223-232

First online:

On the use of splines for the numerical solution of nonlinear two-point boundary value problems

  • R. P. TewarsonAffiliated withApplied Mathematics and Statistics Department, State University of new York at Stony Brook

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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(h 3) to eitherO(h 6) orO(h 7), whereh is the net size. The use of splines leads to solutions that reflect the smoothness of the slopes of the differential equations.