numerically approximate the solution to a first order initial value problem - Maple Programming 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 $\frac{ⅆ}{ⅆt}y\left(t\right)=f\left(t,y\right)$ 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

 > $\mathrm{with}\left(\mathrm{Student}[\mathrm{NumericalAnalysis}]\right):$
 > $\mathrm{InitialValueProblemTutor}\left(\right)$
 > $\mathrm{InitialValueProblemTutor}\left(\frac{ⅆ}{ⅆt}y\left(t\right)=\mathrm{cos}\left(t\right),y\left(1\right)=4.23,t=5\right)$
 > $\mathrm{InitialValueProblemTutor}\left(\frac{ⅆ}{ⅆx}f\left(x\right)=f\left(x\right)-{x}^{2},f\left(0\right)=0.5,x=3\right)$

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