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can't help with matlab
this is your homework - look in your textbook
if your instructor allows it, use google
i think the line "... at equal space intervals t = k delta t..." may be a typo, as space is x, not t
the c in the one dimensional heat equation is a measure of the "thermal diffusivity" - that is, how well energy in the form of heat transfers through the material
choose a value for an insulator from a table in your text
note that the units of c, L, and delta t must be consistent - so meters and seconds, or feet and seconds
L is the length of the rod
it doesn't matter what length you pick, the form of u(x,t) will be the same
delta t is a time interval in seconds
since matlab will be doing the calculations, choose a time interval that won't take forever to calculate, like nanoseconds, and one that may fail to show the time progression, like 1 hour
make matlab do the calculation
x is the position along the rod - first try, start at 0, end at L, and calculate every 0.1 x L
t is the time - first try, start at 0, and then increment by 1 second
loop x = 0 to L in steps of 0.1*L
loop t = 0 to ?? 15 minutes in steps of 1 second
find u(x,t) according to the equation given
end loop t
end loop x
make the graph
how long did matlab run to do the calculation?
have you met the requirements of the problem?
based on those questions, decide if more x intervals or more t intervals or more time may be appropriate