Here is a typienl steedy-state hest fow problesn. consider a thin steel plnte to be 10 x 20 (en垆reetangle. if ane side of the 10 em edge is held ft 100c fund the other three edges are held ntopc, what nre the stendy-state tempersture at interioe points? we ean stute the problem mathematically in this way if w℃ fussume that heat flows only in the znnd y directions: find ,) (temperature) such that with boundnry eoaditions u,0)-0 u(0,8)-0 u(20,g)-100 we repince the differential equntion by a differenee equation which relntes the tempenature t the point ( ) to the temperuture nt four neigh- bouring p ints, ench the distance h swi y from (4,吩. an approximitaan of equation (3) relts when we scleet a set of such points (these sre aften enlled ns nodes) nnd find the solution to the et of differenee equations that result. (n) if we chocse h-& em, find the tempersture nt interior paints (b) write a program to enlealate the tempernture distribution on interior points with h-26, hー0.25, hー0.025 fund hー0.0025 ern. diseuss your solutions fund examine the effeet of grid size h. (c) modiied the difference eqution (4)so that it permits to solve the equntion on the region with boundery coadition u-don ll boandaries except for y-0, where u-1.0 write nd run the progrn numerieal results with different grid sixes hnnd discuss yowr