Accession Number:

AD0618840

Title:

GENERALIZED MULTISTEP PREDICTOR-CORRECTOR METHODS,

Descriptive Note:

Corporate Author:

TECHNISCHE HOCHSCHULE MUNICH (WEST GERMANY)

Personal Author(s):

Report Date:

1963-11-01

Pagination or Media Count:

23.0

Abstract:

The order p which is obtainable with a stable k-step method in the numerical solution of y fx,y is limited to p k 1 by the theorems of Dahlquist. In the present paper the customary schemes are modified by including the value of the derivative at one nonstep point as usual, this value is gained from an explicit predictor. It is shown that the order of these generalized predictor-corrector methods is not subject to the above restrictions stable kstep schemes with p 2k 2 have been constructed for k less than or to 4. Furthermore it is proved that methods of order p actually converge like hp uniformly in a given interval of integration. Numerical examples give some first evidence of the power of the new methods. Author

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Distribution Statement:

APPROVED FOR PUBLIC RELEASE