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 ⅆⅆty⁡t=f⁡t,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
with⁡StudentNumericalAnalysis:
InitialValueProblemTutor⁡
InitialValueProblemTutor⁡diff⁡y⁡t,t=cos⁡t,y⁡1=4.23,t=5
InitialValueProblemTutor⁡diff⁡f⁡x,x=f⁡x−x2,f⁡0=0.5,x=3
See Also
Student[NumericalAnalysis], Student[NumericalAnalysis][InitialValueProblem], Student[NumericalAnalysis][InteractiveOverview]
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