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PYTHON: We want to solve the differential equation df/dx = 2 + exp(x), f(0) = 1in the interval [0, 1]. Divide the interval into N
PYTHON: We want to solve the differential equation df/dx = 2 + exp(x), f(0) = 1in the interval [0, 1].
Divide the interval into N divisions, x0 = 0, x1 = h = 1/N, x2 = 2h = 2/N, , xN = Nh/N = 1, and use df/dx = [f(x+h) f(x)]/h to determine the value of f(x) at x1, x2, , xN.
Calculate the error: assume the exact solution is F(x), and define the error as sum over i from 0 to N of |f(xi) F(xi)|/N.
Do the calculation for N = 10, 20, 30, , 200 and plot the error as a function of N.
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