References

RUNGE-KUTTA METHODS: LOCAL ERROR CONTROL DOES NOT IMPLY GLOBAL ERROR CONTROL


[1] E. Hairer, S. P. Norsett and G. Wanner, Solving Ordinary Differential Equations I: Nonstiff Problems, Springer, Berlin, 2000.

[2] D. Kincaid and W. Cheney, Numerical Analysis: Mathematics of Scientific Computing 3rd Edition, Brooks/Cole, Pacific Grove, 2002.

[3] R. J. LeVeque, Finite Difference Methods for Ordinary and Partial Differential Equations, SIAM, Philadelphia, 2007.

[4] J. S. C. Prentice, Stepwise global error control in an explicit Runge-Kutta method using local extrapolation with high-order selective quenching, Journal of Mathematics Research 3(2) (2009), 126-136.

[5] J. S. C. Prentice, General error propagation in the RKrGLm method, Journal of Computational and Applied Mathematics 228 (2009), 344-354.

[6] J. S. C. Prentice, Relative global error control in the RKQ method for systems of ordinary differential equations, Journal of Mathematics Research (accepted; in press) (2009).