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

Online Help

All Products    Maple    MapleSim


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

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)

Parameters

ODE

-

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

IC

-

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

t

-

name; the independent variable

b

-

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

opts

-

(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

Description

• 

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.

Notes

• 

The Two-Step Adams-Bashforth difference equation is

wi&plus;1&equals;wi&plus;12h3fti&comma;wifti1&comma;wi1

  

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.

Examples

withStudent&lsqb;NumericalAnalysis&rsqb;&colon;

AdamsBashforth&DifferentialD;&DifferentialD;tyt&equals;cost&comma;y0&equals;0.5&comma;t&equals;3&comma;submethod&equals;step2

0.6773

(1)

AdamsBashforth&DifferentialD;&DifferentialD;tyt&equals;cost&comma;y0&equals;0.5&comma;t&equals;3&comma;submethod&equals;step2&comma;output&equals;plot

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