1. Both techniques can be extended to thrne-dimensional problems and both techniques have about eciu:ilrates of convergence for a typical nonliftint; problem. Fr·om the point of view of computer storage requirements and :1dlhmetic-whieh can be crucial consiclerations in a th 1·N,dimensional problem-the velocity potential is a better choice o( dependent val'iable than the v.iluns of u,v,w. Fot· :it n.givcn point in the finite difference, grid, Eqs. (1) n'quirc thr·cC'times !he storage of Eq. (G)and about 2 - 2.5 ns much algebra per· iteration step. (Tf the fully nonlinc,ar inot:itionnl equations arc ronsiclerccl, the r:1.tio of ndlhmctic per step for the two methods drops shat'ply.) How('vcr, p;1si experience with Eq. (G)in two dimensions shows th:ita typical lifting :iirfoil n13.y require 2 - 3 limes ns many iterations as a , nonliftinr; profile. This situation arises because in a velocity potential forrnulntion Uw ci 1:cul:1Hon is nn unknown magnitude which must be specified as pnrt of the bo 1.mdnry conditions; and, g;cnernlly, tho circulation ls found frnn; an addltion:ll iteration process which is built ento tl 1(' overall t·elnxation proccd 11rc, In tht·ee dinicnsic,n, ti,\' dn·ulntion \",t·il': in the sp:1nwise direction and thi, [u,·thcT rornplic:tc-s !lie solution pi·oeess, Thus, one expects that the itr.rativc p!'oCt'Ss to impo.sc the Kutt:1 C"ondition on Eq. (G)will he a difficult pn;(·('ss w!1ich will lower the rate oCconvcrgcricc of the ovci·- all i·claxation procedure.
2. LB2 32 LB1-2 LD2+2 )
3. 1 2 '''j,k,LB2 - 2 wj,k,Lf\2+1 q"° [df(x,v,+O)dx .