# 75 u i j1 1 3 u i j1 u i1 j u i1 j 3 5 5

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Unformatted text preview: 5 1 3 u 3,2 u 3,0 (u 2,1 u 4,1 ) .28506 5 5 similarly u 4,2 .39664, u 5,2 .49922,u 6,2 .59982 u1,2 u 7,2 .69994, u 8,2 .8000, u 9,2 .9000 (ii) Richardson’s Scheme is u i, j1 u i, j1 2r(u i1, j 2u i, j u i1, j ) Put r=0.75 u i, j1 u i, j1 3 u i1, j 2u i, j u i1, j (4) 2 Putting j=1 in (4) u 0,2 0,u10,2 1 3 u1,2 u1,0 (u 0,1 2u1,1 u 2,1 ) .07975 2 3 u 2,2 u 2,0 (u1,1 2u 2,1 u 3,1 ) .2555 2 3 u 3,2 u 3,0 (u 2,1 2u 3,1 u 4,1 ) .27855 2 u 4,2 0.38976, u 5,2 0.49895, u 6,2 0.59985 u 7,2 0.69985, u 8,2 0.8000, u 9,2 0.9000 Table showing a comparision of the values obtained by Dufort‐Frankel and Richardson scheme for second time‐level i=0 i=2 0 Dufort Frankel i=1 i=3 i=4 .1937 .2851 Richardson 0 i=6 i=7 i=8 i=9 i = 10 .0858 i=5 .4992 .6999 1.000 .8000 .9000 .8000 .9000 .3966 .2555 .2886 .0798 .5998 .4990 .3968 .5998 Graphically it is as follows: 1 0.9 Dufort Frankel Richordson 0.8 0.7 u(x.t) 0.6 0.5 0.4 0.3 0.2 0.1 0 0 0.1 0.2 0.3 0.4 0.5 x 0.6 0.7 0.8 0.9 1 .6998 1.000...
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