Interpolants for runge-kutta formulas
WH Enright, KR Jackson, SP Nørsett… - ACM Transactions on …, 1986 - dl.acm.org
ACM Transactions on Mathematical Software (TOMS), 1986•dl.acm.org
A general procedure for the construction of interpolants for Runge-Kutta (RK) formulas is
presented. As illustrations, this approach is used to develop interpolants for three explicit RK
formulas, including those employed in the well-known subroutines RKF45 and DVERK. A
typical result is that no extra function evaluations are required to obtain an interpolant with O
(h 5) local truncation error for the fifth-order RK formula used in RKF45; two extra function
evaluations per step are required to obtain an interpolant with O (h 6) local truncation error …
presented. As illustrations, this approach is used to develop interpolants for three explicit RK
formulas, including those employed in the well-known subroutines RKF45 and DVERK. A
typical result is that no extra function evaluations are required to obtain an interpolant with O
(h 5) local truncation error for the fifth-order RK formula used in RKF45; two extra function
evaluations per step are required to obtain an interpolant with O (h 6) local truncation error …
A general procedure for the construction of interpolants for Runge-Kutta (RK) formulas is presented. As illustrations, this approach is used to develop interpolants for three explicit RK formulas, including those employed in the well-known subroutines RKF45 and DVERK. A typical result is that no extra function evaluations are required to obtain an interpolant with O(h5) local truncation error for the fifth-order RK formula used in RKF45; two extra function evaluations per step are required to obtain an interpolant with O(h6) local truncation error for this RK formula.
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