numerically approximate the solution to a first order initial-value problem with the Adams-Moulton Method - Maple Help

Online Help

All Products    Maple    MapleSim

Home : Support : Online Help : Education : Student Package : Numerical Analysis : Visualization : Student/NumericalAnalysis/AdamsMoulton

Student[NumericalAnalysis][AdamsMoulton] - numerically approximate the solution to a first order initial-value problem with the Adams-Moulton Method

Calling Sequence

AdamsMoulton(ODE, IC, t=b, opts)

AdamsMoulton(ODE, IC, b, opts)




equation; first order ordinary differential equation of the form ⅆⅆtyt=ft,y



equation; initial condition of the form y(a)=c, where a is the left endpoint of the initial-value problem



name; the independent variable



algebraic; the point for which to solve; the right endpoint of this initial-value problem



(optional) equations of the form keyword=value, where keyword is one of numsteps, output, comparewith, digits, plotoptions, or submethod; options for numerically solving the initial-value problem



Given an initial-value problem consisting of an ordinary differential equation ODE, a range a <= t <= b, and an initial condition y(a) = c, the AdamsMoulton command computes an approximate value of y(b) using one of the Adams-Moulton Methods (a family of implicit multi-step methods).


If the second calling sequence is used, the independent variable t will be inferred from ODE.


The endpoints a and b must be expressions that can be evaluated to floating-point numbers. The initial condition IC must be of the form y(a)=c, where c can be evaluated to a floating-point number.


The AdamsMoulton command is a shortcut for calling the InitialValueProblem command with the method = AdamsMoulton option.



The Adams-Moulton implicit difference equation is solved at each step using fsolve, Maple's numeric root-finding routine. For example, if the third-order difference equation



is used, then at each iteration i, this equation will be numerically solved for wi&plus;1. The final wN computed is the approximate value of y(b).


The above equation is also (confusingly) called the "Two-Step" Adams-Moulton difference equation.


To approximate the solution to an initial-value problem using a method other than the Adams-Moulton Method, see InitialValueProblem.







See Also

Student[NumericalAnalysis], Student[NumericalAnalysis][InitialValueProblem], Student[NumericalAnalysis][VisualizationOverview]

Download Help Document

Was this information helpful?

Please add your Comment (Optional)
E-mail Address (Optional)
What is ? This question helps us to combat spam