Interpolation, approximation and differential equations solvers

As step

is positive value of the function

must be less then

. There are two ways to define the best value of step

, the firs one is to define maximum value of function

on the integration area, another way is to use different

for each value

, where

. So integration step is strongly depends on value of

References

1. J. C. Butcher, Numerical methods for ordinary differential equations, ISBN 0471967580

2. George E. Forsythe, Michael A. Malcolm, and Cleve B. Moler. Computer Methods for Mathematical Computations. Englewood Cliffs, NJ: Prentice-Hall, 1977. (See Chapter 6.)

3. Ernst Hairer, Syvert Paul Nørsett, and Gerhard Wanner. Solving ordinary differential equations I: Nonstiff problems, second edition. Berlin: Springer Verlag, 1993. ISBN 3-540-56670-8.

4. William H. Press, Brian P. Flannery, Saul A. Teukolsky, William T. Vetterling. Numerical Recipes in C. Cambridge, UK: Cambridge University Press, 1988. (See Sections 16.1 and 16.2.)

5. Kendall E. Atkinson. An Introduction to Numerical Analysis. John Wiley & Sons - 1989

6. F. Cellier, E. Kofman. Continuous System Simulation. Springer Verlag, 2006. ISBN 0-387-26102-8.

7. Gaussian Quadrature Rule of Integration - Notes, PPT, Matlab, Mathematica, Maple, Mathcad at Holistic Numerical Methods Institute

8. Burden, Richard L.; J. Douglas Faires (2000). Numerical Analysis (7th Ed. ed.). Brooks/Cole. ISBN 0-534-38216-9.

Interpolation, approximation and differential equations solvers (стр. 4 из 4)

References