I have to solve an ivp of the form: du/dt = f(t,u), u(t0) = u0, for a function u = u(t)?R for t=>t0, using Adams Bashforth 2nd order linear multistep method.
I have to write a function file with input t0 = initial time, tf = final time, u01=[u0; u1], n = number of time steps.
And output: t – is vector of length n+1 containing the times t0,t1,…,tn , and u – is a vector of length n+1 with the first element of u being u0 and with the (i+1) the element of u being the approximation ui for i=1,…,n.
So far i have: funtion [t,u]=ivpab2(t0,tf,u01,n) and i know that h=(tf-t0)/n and t(i)=t0+i*h The testing is to be done for the function u'=f(t,u)=-2*u+3*exp(-2*t)cos(3*t) which also needs to be implemented into this function file.
I would be extremely thankful for any help to how to even start with this.
Thank you.
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