Linear multistep method: Difference between revisions

Revision as of 22:12, 17 March 2012

Revision as of 18:48, 18 March 2012

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where ''h'' is the time step (sometimes referred to as <math> \Delta t </math>).

Multistep methods use information from morethe thanprevious one''s'' prior stepsteps to calculate the next value. In particular, a ''linear'' multistep method uses a linear combination of <math>y_i</math> and <math>f(t_i,y_i)</math> to calculate the value of ''y'' for the desired current step. Thus, a linear multistep method is a method of the form

: <math> \begin{align}

& y_{n+s} + a_{s-1} y_{n+s-1} + a_{s-2} y_{n+s-2} + \cdots + a_0 y_n \\