Output in extrapolation codes
Whereas some codes for the numerical integration of the initial value problem, such as the Adams code, are largely influenced by the places at which the user requires an answer because of the feasibility of applying an interpolating polynomial, the same is not true of certain others, such as Runge-Kutta methods. After describing how fixed-output Runge-Kutta codes can be affected by output requirements, the authors show how the work of P. Deuflhard on variable order codes based on extrapolation of the midpoint rule enables a reduction in the sensitivity to output. They also complement Deuflhard's variation of order by deriving ''interpolating'' Runge-Kutta formulae. Numerical results show that the resulting code is much less sensitive to output than existing codes, particularly at cruder tolerances and with relatively dense output.
scientific article; zbMATH DE number 3846775