numerically approximate the solution to a first order initial value problem using Euler's method - Maple Help

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Student[NumericalAnalysis][EulerTutor] - numerically approximate the solution to a first order initial value problem using Euler's method

Calling Sequence

EulerTutor(ODE, IC, t=b)

Parameters

ODE

-

(optional) 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 EulerTutor command launches a tutor interface that computes and plots the numerical approximation to y(b), the exact solution to the given initial-value problem, using Euler's method.

• 

If EulerTutor is called with no arguments, EulerTutor(), it uses a default ordinary differential equation.

• 

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

• 

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

• 

The EulerTutor returns either a plot or a value. For information on how to obtain other return values using the Euler command, see Euler.

• 

The step-by-step calculations in the EulerTutor are only available from within the tutor interface.

Examples

withStudent[NumericalAnalysis]:

EulerTutor

EulerTutorⅆⅆtyt=yt+tcost

EulerTutorⅆⅆtyt=yt+tcost,y0=0.5

EulerTutorⅆⅆtyt=yt+tcost,y0=0.5,t=3

See Also

Student[NumericalAnalysis], Student[NumericalAnalysis][Euler], Student[NumericalAnalysis][InitialValueProblem], Student[NumericalAnalysis][InitialValueProblemTutor], Student[NumericalAnalysis][InteractiveOverview]


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