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C%C" > @`B  Bo?"0@NNN?NB  Bo?"0@NNN?NB  Bo?"0@NNN?NB   Bo?"0@NNN?NH  0޽h ? ̙33___PPT10i.[ڬ+D=' = @B + K0   4(  `  c $A /??@ /  NGBH ?"6@ NNN?NY9< j  # #" ^  Nm ?"6@ NNN?N N        (..) 1.       :  Bi, i=1,2,& k     (            ),   :    ,       (         )         (1)-(2),        ,     . , ,              ,       .,        .I%%I 2  {**R5>PJ2  @`B  Bo?"0@NNN?NB  Bo?"0@NNN?NB  Bo?"0@NNN?NB   Bo?"0@NNN?N`  c $A  ??$E  `  c $A  ?? R  `  c $A  ??$   H  0޽h ? ̙33___PPT10i.[ڬ+D=' = @B +? K0 >6@ (  `  c $A  ??@    NGBH ?"6@ NNN?NY9<:d   #"    N4a ?"6@ NNN?N :  ,       ,         (1)-(2) ,      (principle)                 ,       D      ,                   (  "  " . 217,       ) , ,              "   ,          ""      "  "(Residual Methods), "  "   " (Variational Methods),    M     (Finite Elements Methods).      (trial functions)  :  fi(x), i=1,2,& ,v        ai, i=1,2,& ,  .(%y &$n K  0@$  H (  . /   @`B  Bo?"0@NNN?NB  Bo?"0@NNN?NB  Bo?"0@NNN?NB   Bo?"0@NNN?N`  c $A  ??@  `  c $A  ?? K3   `  c $A  ??G  H  0޽h ? ̙33___PPT10i.[ڬ+D=' = @B + K0   P ,X (  `  c $A  ??@    NGBH ?"6@ NNN?NY9< d j , #" j  N~ ?"6@ NNN?Nj T       ,  . 2.        ,        (R):               .      (       ) :          : ()    (Weighted Residual Methods)        (trial function),  (   ):j%,Z%T@xU&S7 ]  ?) @`B  Bo?"0@NNN?NjB  Bo?"0@NNN?NjB  Bo?"0@NNN?NB   Bo?"0@NNN?Njj`  c $A  ?? +c  `  c $A  ??c ^~   ` ( c $A  ??   H  0޽h ? ̙33___PPT10i.[ڬ+D=' = @B +A K0 @8` (  `  c $A  ??@    NGBH ?"6@ NNN?NY9<< d j  #" j   N ?"6@ NNN?Nj <       (1): ,   h(x)    ,      R(x).             :  Wi(x)  ,                 ( ).           : (i)     (Collocation Method  Col.)           impulse Functions(Dirac):              xi               .B *@6YW j47 K.7@" @B1) @`B  Bo?"0@NNN?NjB  Bo?"0@NNN?NjB  Bo?"0@NNN?NB   Bo?"0@NNN?Njj`  c $A  ??6   `  c $A  ??(& @  `  c $A  ??    H  0޽h ? ̙33___PPT10i.[ڬ+D=' = @B + K0   p x (  `  c $A  ??@    NGBH ?"6@ NNN?NY9< d j  #" j  ND ?"6@ NNN?Nj z:     .. (3)  :    -                   ( ,     ) :       ,      . , ,              , R(x),       , ,     , .  H/2 (    (6)    ).         :  d 3%t% G 'YP@08XB  Bo?"0@NNN?NjB  Bo?"0@NNN?NjB  Bo?"0@NNN?NB   Bo?"0@NNN?Njj`  c $A  ??,T '  `  c $A1 - ??  8  - `  c $A t ??H t H  0޽h ? ̙33___PPT10i.[ڬ+D=' = @B +W K0 VN  (  `  c $A  ??@    NGBH ?"6@ NNN?NY9< d   #"   N ?"6@ NNN?N (,        : ,      ,  :    ,          , : (ii)     (Subdomain Method  S.D.)                 ,   ,              . ,     : :     .. (3),         (6)     , .l%)rF 9 u  A0 @`B  Bo?"0@NNN?NB  Bo?"0@NNN?NB  Bo?"0@NNN?NB   Bo?"0@NNN?N`   c $A  ??U <  `  c $A  ??j(   `  c $A  ??PD   `  c $A  ?? Y   H  0޽h ? ̙33___PPT10i.[ڬ+D=' = @B + K0    (  `  c $A  ??@    NGBH ?"6@ NNN?NY9<> d   #"   N<3 ?"6@ NNN?N >         ,          .. , ,     (8), :       :  :        : (iii)   Galerkin (G.)   ,          () , :             .D_'%  9 @`B  Bo?"0@NNN?NB  Bo?"0@NNN?NB  Bo?"0@NNN?NB   Bo?"0@NNN?N`  c $A ( ??mT  ( `  c $A B ??:2] B `  c $A . ??2  . `  c $A 1 ?? q   1 `  c $A 6 ?? ##  6 H  0޽h ? ̙33___PPT10i.[ڬ+D=' = @B +  K0    (  `  c $A 7 ??@ 7   NGBH ?"6@ NNN?NY9<d   #" ~  NF ?"6@ NNN?N :     .. (3)           (4)   :     W(x)     (trial) :    :        :        Galerkin  :F_m 0 x  @`B  Bo?"0@NNN?NB  Bo?"0@NNN?NB  Bo?"0@NNN?NB   Bo?"0@NNN?N`  c $A E ??n E `  c $A J ??/?  J `  c $A v ??w p v `  c $A R ??    R `  c $A! ] ??V D  ] H  0޽h ? ̙33___PPT10i.[ڬ+D=' = @B + K0   (  `  c $A V ??@ V   NGBH ?"6@ NNN?NY9<0 j  # #"   Nb ?"6@ NNN?N *(iv)      (Least Squares Method-L.S.)                :             : :     .. (3)      (6)                 :         ,  :     (14)          :\F_!EnW  F$7 @`B  Bo?"0@NNN?NB  Bo?"0@NNN?NB  Bo?"0@NNN?NB   Bo?"0@NNN?N`  c $A ` ??D  ` `  c $A c ??b33 2 c `  c $A$ k ??   k `  c $A" n ??Y DDI n `  c $A# s ??(   s H  0޽h ? ̙33___PPT10i.[ڬ+D=' = @B +9 K0 80 (  `  c $A t ??@ t   NGBH ?"6@ NNN?NY9< d   #" `   N$ ?"6@ NNN?N 0 :     :   4      W(x)          ,                 .        F.E.M.      (Variational Methods). (II)     (Variational Method - Var.)           26   ,               ( 43), (42 ), ( 44)    (41)     (42) ."r%>#pA    " 8p " @`B  Bo?"0@NNN?NB  Bo?"0@NNN?NB  Bo?"0@NNN?NB   Bo?"0@NNN?N`   c $A% { ??wg { `  c $A' ~ ??|.  ~ H  0޽h ? ̙33___PPT10i.[ڬ+D=' = @B + K0  d(  `  c $A  ??@    NGBH ?"6@ NNN?NY9<8d   #"    N ?"6@ NNN?N 8            ,         ,          ,  ,        .                                    -.          :  y(0)=y0  y(h)=yH    (    dy/dx)   :   ,     y(x)         .         y*(x)       ,    y*(x)       (16). Z?3WJ  H<^ 8.X<5 @`B  Bo?"0@NNN?NB  Bo?"0@NNN?NB  Bo?"0@NNN?NB   Bo?"0@NNN?N`  c $A(  ??3   `  c $A) 1 ??   1 H  0޽h ? ̙33___PPT10i.[ڬ+D=' = @B + K0 (  `  c $A  ??@    NGBH ?"6@ NNN?NY9< d   #"   NԖ ?"6@ NNN?N ,              ,                      . :     ..(3)    (6),           (17) . To       :  ,    (6)   :    : (18)          ,         . , ,   (18) : |#Z# <*,# BK @`B  Bo?"0@NNN?NB  Bo?"0@NNN?NB  Bo?"0@NNN?NB   Bo?"0@NNN?N`   c $A&  ??  `  c $A*  ??V F   `  c $A+ 3 ??  8  3 `  c $A-  ?? 1    N?"6@ NNN?N iH  0޽h ? ̙33___PPT10i.[ڬ+D=' = @B +i K0 h `   (  `  c $A  ??@    NGBH ?"6@ NNN?NY9<d d   #" (  N ?"6@ NNN?N d        :      : :      (11), (15)  (19)         Galerkin (G.),   (Var.)    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