numerically approximate the solution to a first order initial value problem - Maple Help

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Student[NumericalAnalysis][InitialValueProblemTutor] - numerically approximate the solution to a first order initial value problem

Calling Sequence

InitialValueProblemTutor(ODE, IC, t=b)

InitialValueProblemTutor(ODE)

InitialValueProblemTutor()

Parameters

ODE

-

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

IC

-

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

t

-

(optional) name; the independent variable

b

-

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

Description

• 

The InitialValueProblemTutor command launches a tutor interface that computes, plots, and compares numerical approximations to y(b), the exact solution to the given initial-value problem, using various numerical techniques.

• 

If InitialValueProblemTutor is called with no arguments, InitalValueProblemTutor(), it uses a default initial-value problem.

• 

If IC is not specified, InitialValueProblemTutor uses a default initial condition.

• 

If the t = b argument is not specified, InitialValueProblemTutor uses a default endpoint.

• 

Any of the following methods can be used:

– 

Euler

– 

Taylor

– 

Runge-Kutta Midpoint

– 

Runge-Kutta Order Three

– 

Runge-Kutta Order Four

– 

Runge-Kutta-Fehlberg

– 

Runge-Kutta Heun

– 

Runge-Kutta Modified Euler

– 

Adams-Bashforth Two-Step

– 

Adams-Bashforth Three-Step

– 

Adams-Bashforth Four-Step

– 

Adams-Bashforth Five-Step

– 

Adams-Moulton Two-Step

– 

Adams-Moulton Three-Step

– 

Adams-Moulton Four-Step

– 

Adams-Bashforth-Moulton Second-Order Predictor-Corrector

– 

Adams-Bashforth-Moulton Third-Order Predictor-Corrector

– 

Adams-Bashforth-Moulton Fourth-Order Predictor-Corrector

– 

Adams-Bashforth-Moulton Fifth-Order Predictor-Corrector

Examples

withStudent[NumericalAnalysis]:

InitialValueProblemTutor

InitialValueProblemTutorⅆⅆtyt=cost,y1=4.23,t=5

InitialValueProblemTutorⅆⅆxfx=fxx2,f0=0.5,x=3

See Also

Student[NumericalAnalysis], Student[NumericalAnalysis][InitialValueProblem], Student[NumericalAnalysis][InteractiveOverview]


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