![]() Bashforth, Francis (1883), An Attempt to test the Theories of Capillary Action by comparing the theoretical and measured forms of drops of fluid.In the case of linear multistep methods, a linear combination of the previous points and derivative values is used. Consequently, multistep methods refer to several previous points and derivative values. Multistep methods attempt to gain efficiency by keeping and using the information from previous steps rather than discarding it. Methods such as 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. Single-step methods (such as Euler's method) refer to only one previous point and its derivative to determine the current value. The process continues with subsequent steps to map out the solution. Conceptually, a numerical method starts from an initial point and then takes a short step forward in time to find the next solution point. Linear multistep methods are used for the numerical solution of ordinary differential equations. ![]()
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