u^ (t,x) 5 4 3 2 1 0 1 10 8 6 4 2 0 2 4 6 8 10 0 0.2 0.4 0.6 0.8 1 ‹211› ‹11› ‹212› ‹21› ‹12› ‹1 › t ‹3› c4= 0 ‹4› S2 S3 > T‹3› ‹0› m (T‹3›,x‹3›) u^ 0(x‹3›) ‹2› m'(S2 , x‹0›) m'(S1 , x‹0›) ‹2› ‹1› ‹1› t S‹111› S0 x ‹ 0› S0 ‹0› x h2 h0 ‹0› ‹112› m'(S0 , x‹0›) ‹111› x x‹0› J‹11›=2 S‹2›< T‹2› S1 t S1 ‹3› h1 ‹2 › N=3 N=4 T‹4› ‹22› ‹N› S‹11› c‹12›=0 ‹12› ‹11› J‹1›=2 ‹2› k‹2›< 2k 0 S‹1› ‹1› ‹0› J‹0›=1 0.03 k=k‹0› k0 2k0 0.025 S‹0› 0.02 ‹0› ‹0› bj x ‹ 0› x x ‹ 0› 0.015 0.01 0.005 1 0 2 0.8 3 0.6 4 5 6 x 0.4 7 t 0.2 8 0 9 u (t,x) ^ 0.5 0.4 0.3 x=2 0.03 x=3 0.03 0.1 0 ^ 0. 1 0.02 0.02 0.01 0.01 0.0 0. 2 0 0.2 0.4 0.6 0.8 1.0 t 0.0 0 0.2 0.4 0.6 x=2 0.03 0.2 0.8 1.0 t 0.02 0.02 0.01 0.01 0.0 0 0.2 x=3 0.03 0.4 0.6 0.8 t 1.0 0.0 0 0.2 0.4 0.6 0.8 1.0 0.8 1.0 t 0. 3 0. 4 3 0. 5 10 5 1 0 5 x 10 2 0.015 t 0.01 x=4 0 x = 0,1,-1 x = 0,1,-1 x = 2,-2 x = 2,-2 0.5 0.1 0.5 0.25 0.05 0.25 0.05 0 u 0 0 0 0.25 -0.05 0.25 -0.05 0.5 1 ^ 0 1 3 -0.1 0 x = 3,-3 -2 x10 2 t 1 1 x10 2 3 t x = 4,-4 -3 -0.5 1 0 x10 1 2 3 t 0.1 -0.1 0 x = 3,-3 -2 1 0.5 0.5 0.5 0 u^ 0 0 0 -0.5 -0.5 -0.5 -0.5 -1 5 0 x10 1 2 3 t -1 x = 5,-5 -5 1 0 x10 1 2 3 t -1 x = 6,-6 -6 5 0 x10 1 2 3 t 0.5 -1 x = 5,-5 -5 1 2.5 0.5 2.5 0.5 0 u^ 0 0 0 -2.5 -0.5 -2.5 -0.5 -5 5 0 x10 1 2 3 t x = 7,-7 -8 -1 5 0 x10 1 2 3 t x = 8,-8 -10 -5 1 0 x10 1 2 3 t -1 x = 7,-7 -8 1 2.5 2.5 0.5 0.5 0 u^ 0 0 0 -2.5 -2.5 -0.5 -0.5 -5 0 1 2 3 t -5 0 1 2 3 t -1 0 1 2 3 t -1 x10 1 x10 1 x10 0 2 3 2 3 2 3 t x = 6,-6 -6 0 3 x = 4,-4 -3 0 2 t 1 t x = 8,-8 -10 1 t 0.2 x10 0.4 0.6 0.8 1.0 t -3 x=6 3.0 2.0 2.0 1.0 0.0 t 0.0 0 0.2 x10 0.4 0.6 0.8 1.0 -3 1.0 1.0 0.5 0.0 t 0.0 0.4 0.6 x10 0.05 0.8 1.0 0 0.4 0.6 0.8 1.0 t 0.0 0 0.2 0.4 0.6 0.8 1.0 t 0.0 0 0.2 0.4 0.6 t -3 1.5 x10 x=8 0.2 0.2 x=7 x=6 4.0 x=7 3.0 2.0 2.0 0 2.0 0 0.01 0.0 0 4.0 3.0 x=5 0.01 0.005 0 6.0 x=4 0.015 4.0 0.005 0.0 x=5 8.0 0.2 0.4 0.6 0.8 1.0 t 0.0 0 1.0 0.2 0.4 0.6 0.8 1.0 t t 0.0 0 0.2 0.4 0.6 0.8 1.0 0.8 1.0 -3 x=9 x=8 1.5 x=9 1.0 1.0 0.5 0.5 0.2 0.4 0.6 0.8 1.0 t 0.0 0 0.2 0.4 0.6 0.8 1.0 t 0.0 0 0.2 0.4 0.6 t