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Show 24 Next suppose v changes while u is constant. In this case Fn and Gn are constants and can be thought of as just coefficients in the above equations. Let the correction term for f be Cf and the correction term for g be Cg. Since g is a correction term for f, then C8 is a correction term for Cf· These four numbers can be arranged in a square as shown in figure 4-1. This reresentation will be called a "register-square." Figure 4-1 In the register-square, f is the value of the function at u,v, and g, Cf, and Cg are correction terms. If we move in the v direction then Cf corrects f and Cg corrects g. If we move in the u direction, g corrects f and Cg corrects Cf. Inserting u, v, and the coefficients yields: v9(u3al + uZb, + uCI + d.) h2[v3(3a,u + +v2(ula7 + uZb2 + b,) uCz + dz) + v(u3a3 + u2b3 + uC3 + d3) +v2(3azu + bz) + (u3ac + u2bc + uc, + de) +v(3a3u + b3) + «3a4u + b4)] k2[3v(u3al + u2bl + UCI + d,) h2kZ[3v(3a IU + b I) +(u3az + uZbz + UCz + dz)] + (3azu + b2)] |
