(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Consider dy/dx=x+y, a function of both x and y subject to initial condition, y(x_{0})=y_{0}.

Use Taylor series to determine y(x_{0}+[itex]\Delta[/itex]x) to 4th order accuracy.

Initial condition: x_{0}=0, y(x_{0})=1

step size: [itex]\Delta[/itex]x=0.1

Show 5 significant digits in the answer.

2. Relevant equations

[itex]\epsilon[/itex]=O([itex]\Delta[/itex]x^{5})

Do the calculations for only one step.

3. The attempt at a solution

dy/dx=f(x,y)

Taylor series:

y(x_{0}+[itex]\Delta[/itex]x)=y(x_{0})+[itex]\Delta[/itex]xf(x_{0},y(x_{0}))+[itex]\epsilon[/itex]

My solution:

f(x_{0},y(_{0}))=f(0,1)=0+1=1

y(0+0.1)=1+0.1(1)+.00001=1.10001

Does this seem correct. It feels like I missed something. On the other hand it makes sense. Did I miss something or mess up a step?

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# Tayor series with truncation error

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