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

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

Calling Sequence

AdamsBashforth(ODE, IC, t=a..b, opts)

AdamsBashforth(ODE, IC, a..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 AdamsBashforth command computes an approximate value of y(b) using one of the Adams-Bashforth Methods (a family of explicit 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 AdamsBashforth command is a shortcut for calling the InitialValueProblem command with the method = AdamsBashforth option.



The Two-Step Adams-Bashforth difference equation is



and is also called the second-order Adams-Bashforth difference equation.


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







See Also

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

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