论文信息 - Quadrature and Runge-Kutta formulas

Quadrature and Runge-Kutta formulas

Error estimation and step size adjustment procedures for many high order Runge-Kutta methods fail dramatically when applied to an equation of the form y'(x)=f(x). A practical remedy is proposed and its use exemplified with the Fehlberg [7,8] formulas. The management of storage for this important example is also discussed.

L. F. Shampire

[1] J. H. Verner,et al. Some Explicit Runge”Kutta Methods of High Order , 1972 .

[2] T. E. Hull. NUMERICAL SOLUTIONS OF INITIAL VALUE PROBLEMS FOR ORDINARY DIFFERENTIAL EQUATIONS , 1975 .

[3] R. Kalaba,et al. An initial-value method for integral operators V. Kernels depending upon a parameter , 1975 .

[4] Runge-Kutta Methods with Constrained Minimum Error Bounds* , 1966 .

[5] H. L. Ingram. A comparison of digital computer programs for the numerical solution of ordinary differential equations , 1973 .

[6] H. A. Luther. An explicit sixth-order Runge-Kutta formula , 1968 .

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

[8] W. F. Powers,et al. Numerical integration aspects of a nutrient utilization ecological problem , 1974 .

[9] A. R. Curtis. High-order Explicit Runge-Kutta Formulae, Their Uses, and Limitations , 1975 .

[10] An initial-value method for integral operators—IV. Complex-valued kernels of laser theory , 1973 .

[11] H. A. Luther. Further explicit fifth-order Runge-Kutta formulas. , 1966 .