A Note About Overhead Costs in ODE Solvers

It is shown that the number of function evaluations by itself is not an adequate measure of cost of solving ordinary differential equations because of the large overhead costs m Adams codes except when the function is very expensive to evaluate or when the codes being compared are sinnlar. Because of these large overhead costs in Adams codes, it may be more economical to use a good Runge-Kut ta code than an Adams code m many apphcation environments.

[1]  Phyllis Fox,et al.  A comparative study of computer programs for integrating differential equations , 1972, CACM.

[2]  W. H. Enright,et al.  Test Results on Initial Value Methods for Non-Stiff Ordinary Differential Equations , 1976 .

[3]  J. M. Watt.  Numerical Initial Value Problems in Ordinary Differential Equations , 1972 .

[4]  T. E. Hull,et al.  Comparing Numerical Methods for Ordinary Differential Equations , 1972 .

[5]  Michael A. Malcolm,et al.  Computer methods for mathematical computations , 1977 .

[6]  T. E. Hull,et al.  A Theoretical Criterion for Comparing Runge–Kutta Formulas , 1978 .

[7]  L. Shampine,et al.  Computer solution of ordinary differential equations : the initial value problem , 1975 .

[8]  Lawrence F. Shampine,et al.  A User’s View of Solving Stiff Ordinary Differential Equations , 1979 .

[9]  Lawrence F. Shampine.  Stability properties of Adams codes , 1978, TOMS.

[10]  F. T. Krogh.  Variable order integrators for the numerical solution of ordinary differential equations , 1971 .

[11]  Fred T. Krogh,et al.  On Testing a Subroutine for the Numerical Integration of Ordinary Differential Equations , 1973, JACM.

[12]  A. Sedgwick,et al.  An effective variable-order variable-step adams method. , 1973 .

[13]  H. A. Watts,et al.  Solving Nonstiff Ordinary Differential Equations—The State of the Art , 1976 .

[14]  F. Grund.  Forsythe, G. E. / Malcolm, M. A. / Moler, C. B., Computer Methods for Mathematical Computations. Englewood Cliffs, New Jersey 07632. Prentice Hall, Inc., 1977. XI, 259 S , 1979 .