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Numerical Differential Equation.

MathematicalPhysicist
Gold Member
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give a numerical method of order bigger or equals 2 for the numerical solution of:
y'''(x)+2xy'(x)+e^(y(x))=cos(x)
in the interval: [0,1] with boundary conditions:
y(0)=1,y(1)=2,y'(0)=0

Attempt at solving:
well I thought of difference equation:
[/tex]y_{n+3}+2x_ny_{n+1}+e^{y_n}=cos(x_n)[/tex]
with y_0=1 and y_N=2 where we divide the interval [0,1] with N points of difference:
h=1/N.
Now we want the order would be greater than or equals 2, i.e the error of y_n+3-y(x_n+3) would be of O(h^3) at least.

where [/tex]y(x_{n+3})=y((n+3)*h)[/tex]
So now I need to expand y through taylor's expansion and then find the error y_n+3-y(x_n+3), I think that I also need to expand e^(y_n) and cos(x_n) through taylor's expansion, am I missing something or as I stated it, it's that much easy?

thanks in advance.
 

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