Linear multistep method: Difference between revisions

Revision as of 22:01, 5 January 2011

Revision as of 01:13, 6 January 2011

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{{redirect|Adams method|the electoral apportionment method|Method of smallest divisors}}

'''Linear multistep methods''' are used for the [[numerical ordinary differential equations|numerical solution of ordinary differential equations]]. Conceptually, a numerical method starts from an initial point and then takes a short '''step''' forward in time to find the next solution point. The process continues with subsequent steps to map out the solution. Single-step methods (such as [[Euler's method]]) refer to only one previous point and its derivative to determine the current value. Methods such as [[Runge–Kutta methods|Runge-Kutta]] take some intermediate steps (for example, a half-step) to obtain a higher order method, but then discard all previous information before taking a second step. Multistep methods attempt to gain efficiency by keeping and using the information from previous steps rather than discarding it. Consequently, multistep methods refer to several previous points and derivative values. In the case of ''linear'' multistep methods, a [[linear combination]] of the previous points and derivative values is used.

==Definitions==