How can I create a differnce equation from a differential equation? The step size h is not given and should stay a variable. For example $y' = y^2 + x^2$ with the known value $y(1) = 2$
convert a ordinary differential equation to a recurrence relation
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ordinary-differential-equations
numerical-methods
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1Depends. What numerical method are you using? Euler? Heun? Runge-Kutta? – 2012-02-08
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0If you are thinking "relatively" small $h$ and looking for approximate solutions, then write $y'(x) \approx \frac{y(x+h)-y(x)}h$. So $y(x+h) \approx y(x) + hx^2 + hy(x)^2$ – 2012-02-08
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0We are using the Euler method. – 2012-02-08