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View Code? Open in Web Editor NEWJupyter notebook class notes for Numerical Methods for PDEs
License: Creative Commons Attribution 4.0 International
Jupyter notebook class notes for Numerical Methods for PDEs
License: Creative Commons Attribution 4.0 International
Dear @mandli,
when I learn the 03 finite_differences file, I could not understand the part of Error Analysis. Could you give me some help? thanks!!Please forgive me for asking some naive questions since I'm new to this area. Here is the list of questions :
error.append(numpy.linalg.norm(numpy.abs(f_prime(x_hat + delta_x[-1]) - f_prime_hat), ord=numpy.infty))
f_prime_hat[0] = (-3.0 * f(x_hat[0]) + 4.0 * f(x_hat[1]) + - f(x_hat[2])) / (2.0 * delta_x[-1]) f_prime_hat[-1] = ( 3.0 * f(x_hat[-1]) + -4.0 * f(x_hat[-2]) + f(x_hat[-3])) / (2.0 * delta_x[-1])
@xh2277 and I find that:
Calculating the error there is a
And the reason we get first order is that we have the step of " Use first-order differences for points at edge of domain"
if we remove the last point of the f_prime_hat.
we will get
by just dropping the last point of f_prime_hat
error.append(numpy.linalg.norm(numpy.abs(f_prime(x_hat[:1] + 0.5 * delta_x[-1]) - f_prime_hat[:1]), ord=numpy.infty))
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