Class of iterative numerical methods for solving differential equations
"Adams' method" redirects here. For the electoral apportionment method, see Method of smallest divisors.
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Linear multistep methods are used for the 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 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.
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Linearmultistepmethods are used for the numerical solution of ordinary differential equations. Conceptually, a numerical method starts from an initial...
Euler method. This line of thought can be continued to arrive at various linearmultistepmethods. The local truncation error of the Euler method is the...
quadrature) numerical methods. Explicit examples from the linearmultistep family include the Adams–Bashforth methods, and any Runge–Kutta method with a lower...
&1\\\end{array}}} The method can also be seen as a linearmultistepmethod with one step. It is the first method of the family of Adams–Moulton methods, and also...
it restricts the usefulness of linearmultistepmethods for stiff equations. An example of a second-order A-stable method is the trapezoidal rule mentioned...
interest here are parallel-in-time multigrid methods: in contrast to classical Runge–Kutta or linearmultistepmethods, they can offer concurrency in temporal...
{\displaystyle y'(x)=0} . A linearmultistepmethod is zero-stable if all roots of the characteristic equation that arises on applying the method to y ′ ( x ) = 0...
a family of implicit methods for the numerical integration of ordinary differential equations. They are linearmultistepmethods that, for a given function...
General linearmethods — a class of methods encapsulating linearmultistep and Runge-Kutta methods Bulirsch–Stoer algorithm — combines the midpoint method with...
Adams method may refer to: A method for the numerical solution of ordinary differential equations, also known as the linearmultistepmethod A method for...
In numerical analysis, the local linearization (LL) method is a general strategy for designing numerical integrators for differential equations based...
Linearmultistepmethod, schemes used in mathematics to find numerical solutions of ordinary differential equations Mixed model, also called linear mixed...
and linearmultistepmethods. However, to acquire at least second-order accuracy and unconditional stability, the scalar parameters of each method and...
use any of the numerical integration methods, such as Euler–Maruyama method, Heun's method, linearmultistepmethods, etc. Just as in the discrete case...
Runge-Kutta discretizations, linear multistepmethods or a variety of other options. Exponential Rosenbrock methods were shown to be very efficient in...
priority in discovery of the planet. The search was begun by a laborious method on 29 July. Only after the discovery of Neptune on 23 September 1846 had...
fabricated using multistep low yield processes such as micro-moulding, solid freeform fabrication, and mask lithography. However, these methods require manual...
Jay (2015). Linear Algebra Done Right (3rd ed.). Springer. ISBN 978-3-319-11079-0. Bareiss, Erwin (1968), "Sylvester's Identity and Multistep Integer-Preserving...
reactions required to go from the starting materials to the products in a multistep sequence. This concept is very important when trying to optimize a synthetic...
{\displaystyle {\frac {L}{c}}k(0.05),\ k=0,\dots ,5,} using an 8th-order multistepmethod, the 6 states displayed in figure are found: The red curve is the initial...
regulators. Multistep regulators control the field current to maximize the charging effectiveness (time to charge) and battery life. Multistep regulators...
system. Then it is solved by multistepmethods such as the Euler method, midpoint method or Gragg's modified Midpoint method. These all require solution...