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Download Conference on Applications of Numerical Analysis: Held in by Richard Bellman (auth.), John Ll. Morris (eds.) PDF

By Richard Bellman (auth.), John Ll. Morris (eds.)

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Extra resources for Conference on Applications of Numerical Analysis: Held in Dundee/Scotland, March 23–26, 1971

Example text

Schr~der [60] gave the following generalization method. one has the Suppose there exist two operators Hj(~,~) problems. O. (j = 1,2) defined in DxD which are syntone in % and antitone in ~ . 13) HI(~, ~) ~ T ~ ~ H2(~,~) and I ~ ~ for all ~ e " D D. 14) I n = 0,I,2,... Wn+ 1 = H2(Wn,Vn) starting with the elements Vo,W o g D. 3) are satisfied and that the operator T is completely continuous. 15) v 1•uKw I . 16) u(x) = T u ( x ) = ~o u 1 + tulxIt dt 1+x I we can choose Hj(~,:) = H(~,:) = ~o 1+t ~ (x) 1+x :(t) dt .

1 . 1 . A = [-I, Jl[v) +1] , g donn~e dans L 2 [ ~ ] = l[g,V)L2(~)l 27 Exemple 2 . 1 . 2 A = [0, Jl[V) + 1 ] , g donn~e darts L2(~] ='(g,v]t2[~ ] + (Rappelons qua X = max { X , O } ) . 2. 2. 3. UNE TROISIEME FAMILLE L e ( L 2 [ ~ ] ) n , Sv = [DlV, Notons que S v [ x ) = grad v ( x ) .. '' OnV] Cn L et que[p,Sv]= quand v s Hl [ ~ ] . [ [#i,DiV)L2[~) i=1 Exemple 2 . Oiv[x)dx i=1 d'oO en utilisant l'in@galit@ de Cauchy Schwarz dans(R n f~,Sv] ~ f~lp(x)l)RnIgrad v(x] ~V p s A l~n dx ~ %~Igrad v(x] O'autre part, si X g est d@~ini par : Ol.

6) VoW. 1). 9) is syntone for i = I and antitone a) Let J<2 = O, and ~(x,t) = for i = 2. ~1(x,t) ~ 0 in BxB. 7). 3)] to D. b) In the case ~I = O, we obtain field-approximation J. Schr~der [60] gave the following generalization method. one has the Suppose there exist two operators Hj(~,~) problems. O. (j = 1,2) defined in DxD which are syntone in % and antitone in ~ . 13) HI(~, ~) ~ T ~ ~ H2(~,~) and I ~ ~ for all ~ e " D D. 14) I n = 0,I,2,... Wn+ 1 = H2(Wn,Vn) starting with the elements Vo,W o g D.

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