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

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Student[NumericalAnalysis][RungeKutta] - numerically approximate the solution to a first order initial-value problem with the Runge-Kutta Method

Calling Sequence

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

RungeKutta(ODE, IC, 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 RungeKutta command computes an approximate value of y(b) using the Runge-Kutta 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 RungeKutta command is a shortcut for calling the InitialValueProblem command with the method = rungekutta option.

Notes

• 

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

Examples

withStudent&lsqb;NumericalAnalysis&rsqb;&colon;

RungeKutta&DifferentialD;&DifferentialD;tyt&equals;cost&comma;y0&equals;0.5&comma;t&equals;3&comma;submethod&equals;rk4

0.6411

(1)

RungeKutta&DifferentialD;&DifferentialD;tyt&equals;cost&comma;y0&equals;0.5&comma;t&equals;3&comma;submethod&equals;rk4&comma;output&equals;plot

See Also

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


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