Predictor–corrector method: Difference between revisions

Revision as of 21:26, 26 February 2010

Revision as of 21:27, 26 February 2010

Line 15:

: <math> y' = f(t,y), \quad y(t_0) = y_0. </math>

firstFirst calculate an initial guess value <math>\tilde{y}_{g}</math> via Euler:

: <math>\tilde{y}_{g} = y_i + h f(t_i,y_i)</math>

nextNext, improve the initial guess through iteration of the trapezoidal rule,. thisThe iteration process normally converges quickly:.

: <math>\tilde{y}_{g+1} = y_i + \frac{h}{2}(f(t_i, y_i) + f(t_{i+1},\tilde{y}_{g})).</math>