#8245: tutorial: typo in section "Euler’s Method for Systems of Differential
Equations"
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Reporter: mvngu | Owner: mvngu
Type: defect | Status: new
Priority: minor | Milestone: sage-4.8
Component: documentation | Keywords: beginner
Work_issues: | Upstream: N/A
Reviewer: | Author:
Merged: | Dependencies:
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Description changed by kcrisman:
Old description:
> From [http://groups.google.com/group/sage-
> support/browse_frm/thread/437ae27f84e3a05 sage-support]:
> {{{
> In the section, "A Guided Tour"->"Basic Algebra and Calculus"-
> >"Euler’s Method for Systems of Differential Equations", I found that
>
> the answer of the example is z(1)≈0.75, which seems to be wrong.
>
> The calculation is
> ------------------------------------------------------------------------
> sage: t,x,y = PolynomialRing(RealField(10),3,"txy").gens()
> sage: f = y; g = -x - y * t
> sage: eulers_method_2x2(f,g, 0, 1, 0, 1/4, 1)
> t x h*f(t,x,y) y
> h*g(t,x,y)
> 0 1 0.00
> 0 -0.25
> 1/4 1.0 -0.062
> -0.25 -0.23
> 1/2 0.94 -0.12
> -0.48 -0.17
> 3/4 0.82 -0.16
> -0.66 -0.081
> 1 0.65 -0.18
> -0.74 0.02
> ------------------------------------------------------------------------
>
> So I think the right answer should be z(1)≈0.65
> }}}
New description:
From [http://groups.google.com/group/sage-
support/browse_frm/thread/437ae27f84e3a05 sage-support]:
{{{
In the section, "A Guided Tour"->"Basic Algebra and Calculus"-
>"Euler’s Method for Systems of Differential Equations", I found that
the answer of the example is z(1)≈0.75, which seems to be wrong.
The calculation is
------------------------------------------------------------------------
sage: t,x,y = PolynomialRing(RealField(10),3,"txy").gens()
sage: f = y; g = -x - y * t
sage: eulers_method_2x2(f,g, 0, 1, 0, 1/4, 1)
t x h*f(t,x,y)
y h*g(t,x,y)
0 1 0.00
0 -0.25
1/4 1.0 -0.062
-0.25 -0.23
1/2 0.94 -0.12
-0.48 -0.17
3/4 0.82 -0.16
-0.66 -0.081
1 0.65 -0.18
-0.74 0.022
------------------------------------------------------------------------
So I think the right answer should be z(1)≈0.65
}}}
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/8245#comment:3>
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