Linear multistep method: Difference between revisions

Revision as of 06:58, 6 May 2012

Revision as of 10:20, 8 July 2012

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The Adams–Moulton methods with ''s'' = 0, 1, 2, 3, 4 are ({{harvnb|Hairer|Nørsett|Wanner|1993|loc=§III.1}}; {{harvnb|Quarteroni|Sacco|Saleri|2000}}):

* <math> y_n = y_{n-1} + h f(t_n,y_n) \, </math> — this is the [[backward Euler method]];

* <math> y_{n+1} = y_n + \tfrac12 h \big( f(t_{n+1},y_{n+1}) + f(t_n,y_n) \big) </math> — this is the [[trapezoidal rule (differential equations)|trapezoidal rule]];

* <math> y_{n+2} = y_{n+1} + h \big( \tfrac5{12} f(t_{n+2},y_{n+2}) + \tfrac23 f(t_{n+1},y_{n+1}) - \tfrac1{12} f(t_n,y_n) \big); </math>