1) for an input test, define function, where the function defines an ODE so the following code works:
if type(f) !=function:
return("'f' has be a function")
2) Help me figure out why the following code says there is an error even if qn is in fact a vector:
if type(qn) !=[login to view URL]:
return("'qn' has to be a numpy array")
3) Show that the local truncation error of the single step algorithm is fourth order by checking the error in solving a single step of the IVP
dq/dt = t − q, q(0) = 0 ⇒ q(t) = exp(−t) + t − 1
converges at the expected rate as the timestep is modified. The convergence rate should be shown as a plot. Plot the error against dt, using an appropriate scale. By fitting an appropriate curve to the data using polyfit, which should also be plotted, give evidence to show that the single step algorithm is converging at fourth order.
4) Implement the implicit Gauss-Radau algorithm usng either the root or fsolve function (attached in the file)
5) (optional) document all code
I have also uploaded all my code so far.
Needs to be done within the next 36 hours
Hello, how are you? I am an expert in Mathematics and Physics and Python Programming. I have a lot of experiences in Numerical methods. So I think I can help you. Kindly contact with me. Thanks.
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Hello, How are you? I read your project detail carefully. I know numerical methods like as RK method, GR algorithm... I can help you well. Please contact with me. thanks. Nikita.
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