Question

1) (15 marks) Consider the following PDHE Uz(0, t) = 0, u(5,t)=1, t>0 u(x, 0)- 20 exp(-2), 0<x<!5 (a) Solve using separation of variables. You may leave the eigenfunction expansion coef (b) Plot the solution at t-1,3,5 and 30, along with the initial condition and steady state ficients in inner product form. solution, using 15 terms in your truncated expansion. You may use mupad to evaluate the eigenfunction expansion coefficients from part (a) which you left in inner product form

Answer 1

Here , we our e -Given CPDC) ec) Bounday-cordiler, u,@d)-о, ućst)-i i.slw Conside w (xit) ω (s,t)-1 Otio om ) 9S

ow in unchon non-Ho mogenous PA or Nouo wrtn Tc on-Homogenous Ll It

for Re G) U, C지 t ) , " fox) Consent C. euill xrx) m2 Cre

re Nous net we have tra nsfore

JSSoln One neo to Soln -t wvhich Homogenous haat on ven