Accession Number : AD0618840

Title :   GENERALIZED MULTISTEP PREDICTOR-CORRECTOR METHODS,

Corporate Author : TECHNISCHE HOCHSCHULE MUNICH (WEST GERMANY)

Personal Author(s) : Gragg,William B. ; Stetter,Hans J.

Report Date : NOV 1963

Pagination or Media Count : 23

Abstract : The order p which is obtainable with a stable k-step method in the numerical solution of y' = f(x,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 h(p) uniformly in a given interval of integration. Numerical examples give some first evidence of the power of the new methods. (Author)

Descriptors :   (*NUMERICAL METHODS AND PROCEDURES, OPTIMIZATION), DIFFERENTIAL EQUATIONS, NUMERICAL INTEGRATION, ERRORS, MATHEMATICAL PREDICTION, OPERATORS(MATHEMATICS)

Distribution Statement : APPROVED FOR PUBLIC RELEASE