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

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

Calling Sequence

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

Euler(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, or plotoptions; 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 Euler command computes an approximate value of y(b) using the classical forward Euler method.

• 

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 Euler command is a shortcut for calling the InitialValueProblem command with the method = euler option.

Notes

• 

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

Examples

withStudent&lsqb;NumericalAnalysis&rsqb;&colon;

Euler&DifferentialD;&DifferentialD;tyt&equals;cost&comma;y0&equals;0.5&comma;t&equals;3

1.234

(1)

Euler&DifferentialD;&DifferentialD;tyt&equals;t2&comma;y1&equals;3.10&comma;t&equals;4&comma;output&equals;Error

4.320

(2)

Euler&DifferentialD;&DifferentialD;tyt&equals;cost&comma;y0&equals;0.5&comma;t&equals;3&comma;output&equals;plot

See Also

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


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