Ecuaciones Diferenciales Parciales
December 2, 2022 | Author: Anonymous | Category: N/A
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@APDAGLO@Q NGE@R@OAGDC@Q VDRAGDC@Q PHRB-2626
@APDAGLO@Q NGE@R@OAGDC@Q VDRAGDC@Q D VDR^GR N@ C HLN@CDAGÑO N@ E@OÑH@OLQ EÈQGALQ @audagño n` Adclrnge`r`oagdc`s pdragdc`s hds `stungdnds `s; Pod n` cds `audaglo`s Ty
Tx
δ
Tz
8 Al`egag`ot` n` ngeusgvgndn tçrhgad
j 8 al`egag`ot` n` alonuatgvgndn tçrhgad p 8 n`osgndn n`c hdt`rgdc Ap 8 Adpdagndn adclrèegad n`c hdt`rgdc ^ 8 t`hp`rdturd t8 tg`hpl
@std `audagño n`sargb` cd alonuaagño n` adclr d trdvçs n` uo hdt`rgdc `o rçigh`o trdosgtlrgl `o sus 1 ngh`osgño.
@audagño n` ngeusgño Ay
Ax
N 8 Al`egag`ot` n` ngeusgvgndn A 8 aloa`otrdagño Az Ecugnl
R`pr`s`otd cd ngeusgño hlc`aucdr n` hdsd `otr` ecugnls `o sus 1 ngh`osglo`s.
OL^D; R`pdsdr `c bdcdoa` n` nlon` s` lbtg`o` cds `audaglo`s
Ngstrgbuagño `o `stdnl `stdaglodrgl qu` pu`n`o adrdat`rgzdrs` adrdat`rgzd rs` plr @NV `cèptgads. d) Ngstrgbuagño n` t`hp`rdturd slbr` uod pcdad adcg`ot`.
d) Bdrrd cdrid y n`cidnd qu` `stä dgscdnd, `xa`ptl `o sus `xtr`hls. Cd ngoähgad n` cd ngstrgbuagño uogngh`osglodc n` t`hp`rdturd d cl cdril n` cd bdrrd pu`n` n`sargbgrs` h`ngdot` uod @NV pdrdbñcgad. b) Cd slcuagño, qu` alosgst` `o ngstrgbuaglo`s ngstrgbuaglo `s alrr`splong`ot`s dc `stdnl n` cd bdrrd `o nge`r`ot`s hlh`otls.
EGOG^DQ; NGE@R@OAGDQ @APDAGLO@Q VDRDBÑCGADQ • •
•
HÇ^LNL @]VCGAG^L HÇ^LNL GHVCÈAG^L HÇ^LNL ARDOJ-OGALCQL ARDOJ-OGALCQLO O
•
HÇ^LNL
Qg s` @]VCGAG^L sustgtuy`o cds n`rgvdnds pdragdc`s plr sus dprlxghdaglo`s `o nge`r`oagds egogtds; @audagño n` Adclr
Nge`r`oagds egogtds mdagd dn`cdot` Nge`r`oagds egogtds a`otrdc`s
R`hpcdzdonl `o cd `audagño n` adclr t`o`hls cd sgiug`ot` `audagño dci`brdgad;
Alonuaagño n` adclr `o uod bdrrd dgscdnd; uod bdrrd dgscdnd cloigtungodch`ot` y n` cloigtun C huy Alosgn`r`hls irdon` `o alhpdrdagño alo su irlslr, cd cloigtun n` cd bdrrd s` h`ngrä alo cd vdrgdbc` x, sg`onl `o sus `xtr`hls x 8 6 y x 8 C. Q`do dn`häs cd sgiug`ot`s alongaglo`s; d) ^(x,6) 8 e(x)
63x3C
6) Alongagño Gogagdc (@o t 8 6)
b) ^(6,t) 8 i4(t) t ? 6
Alongagño n` erlot`rd 4 (@o x 8 6)
a) ^(C,t) 8 i2(t) t ? 6
Alongagño n` erlot`rd 2 (@o x 8 C)
^(x4,t4) ^(x4,t2)
^(x2,t4) ^(x2,t2)
^(x4,thdx) ^(x2,thdx)
^(xo,t4) ^(xo,t2) ^(xo,thdx)
R`slcv`r `st` prlbc`hd ouhçrgadh`ot`, sgiogegad `oalotrdr cls vdclr`s n` ^ `o puotls s`c`aaglodnls `o cd bdrrd x4, x2 , … , xo d ag`rtls tg`hpls `salignls t4 3 t2 …. 3thdx
Cd elrhd n` dodcgzdr `c prlbc`hd `s iräegadh`ot`, r`pr`s`otdonl `c nlhgogl n` n`egogagño ^ alhl `c r`atäoiucl qu` s` gcustrd `o `c sgst`hd allrn`odnl x-t n` cd egiurd goe`rglr. g oe`rglr.
^(x2,t2)
Olnls; R`pr`s`otdonl cls olnls `o uod r`n alostrugnd `o `c nlhgogl n` n`egogagño
@k`ragagl 4 ;R`slcv`hls `c prlbc`hd pcdot`dnl, alo uod t`hp`rdturd d tg`hpl tg `hpl a`rl n` -46¶A, y n`spuçs alo uod t`hp`rdturd >6¶A;
Qlcuagño; Vrgh`rl; Alostrughls cd hdccd `o `c nlhgogl n` n`egogagño, pdrd `ccl subngvgnghls tg`hpl y cd cloigtun c loigtun C 8 6,> h, `o >`csubgot`rvdcls n` 6,4 h`o vdrgls subgot`rvdcls. ^ 8 4 m, `o 46 subgot`rvdcls n` 6,4 m t
k
> A » 6 > 8 ) t , 6 ( ^ 4 E A
A » 6 > 8 ) t , > , 6 ( ^
1
^(g,k+4)
2
^(g,k)
4 6
2 E A
^(g+4,k)
g 6
4
2
1
>
x
AG ^(x,6) 8 -46»A
Udclr`s n` ^ `o adnd olnl
A » 6 > 8 ) t , 6 ( ^ 4 E A
t k >6»A
>6»A
>6»A
>6»A
^(g,k+4)
>6»A
>6»A
^(g,k)
>6»A
^(g+4,k)
>6»A g
^(g-4,k) >6»A Qgoiucdr r Olnl Qgoiucd ^(>6+(-46))/2 8 40»A
-46»A
A » 6 > 8 ) t , > , 6 ( ^ 2 E A
x -46»A -46»A -46»A AG ^(x,6) 8 -46»A
-46»A Qgoiucdr Olnl Qgoiucdr
AG ^(x,6)
46 A
^ 8 40»A
Psdonl cd `audagño mdccdnd dot`rglrh`ot`;
t
k
>6»A
>6»A
Vdrd `c olnl g 8 4, k 8 6;
>6»A
>6»A
g >6» A -46»A
-46»A
-46»A
-46»A
-46»A
x
t
Vdrd `c olnl g 8 2, k 8 6;
k
>6»A
>6»A
>6»A
>6»A
g >6»A
-46»A
-46»A
t
-46»A
-46»A
-46»A
x
k
>6»A
Vdrd `c olnl g 8 1, k 8 6;
>6»A
>6»A
>6»A
g >6»A
x
46 A
46 A
46 A
46 A
N` `st` hlnl adcaucdhlst cls vdclr`s n` ^ n` cd s`iuond egcd n` olnls. k >6»A
>6»A
>6»A A » 6 > 8 ) t , 6 ( ^ 4 E A
>6»A
>6»A
>6»A
A » 6 > 8 ) t , > , 6 ( ^
>6»A
40»A
-46»A
40»A
2 E A
>6»A g x
40»A
-46»A
-46»A
-46»A
40»A
46 A
AG ^(x,6) 8 -46 A
Dmlrd n`b`rèdhls adcaucdr cls vdclr`s n` ^ pdrd cd t`ra`rd egcd y cu`il pdrd cd audrtd y dsè mdstd t`rhgodr cds 46 egcds `o qu` subngvgnghls cd mlrd. Vdrd `c olnl g 8 4, k 8 4;
•
HÇ^LNL GHVCGAG^L
@audagño n` Adclr Nge`r`oagds egogtds a`otrdc`s
Qustgtuy`onl
nlon`
Alonuaagño n` adclr `o uod bdrrd dgscdnd @k`ragagl 2 ; R`slcv`hls `c prlbc`hd pcdot`dnl `o cd s`aagño dot`rglr;
t k
A » 6 > 8 ) t , 6 ( ^ 4 E A
>6»A
>6»A
>6»A
>6»A
>6»A
>6»A ^(g-4,k) ^(g,k)
>6»A Qgoiucdr r Olnl Qgoiucd ^(>6+(-46))/2 8 40»A
>6»A
-46»A
^(g+4,k)
>6»A g
^(g,k-4) -46»A
-46»A
A » 6 > 8 ) t , > , 6 ( ^ 2 E A
x -46»A
-46»A Olnl Qgoiucdr
^(>6 ( 46))/2 40 A
AG ^(x,6) 8 -46»A
^ 8 40»A
t
k
Vdrd `c olnl g84, k84
>6»A
>6»A
>6»A
>6»A
>6»A
>6»A
>6»A
>6»A >6»A
>6»A
t
Vdrd `c olnl g82, k84
-46»A
-46»A
k
>6»A
>6»A
>6»A
>6»A
>6»A
>6»A
>6»A
>6»A
g
-46»A
-46»A
-46»A
g x
>6»A
>6»A
-46»A
-46»A
-46»A
-46»A
x
-46»A
Vdrd `c olnl g81, k84
t
k
>6»A
>6»A
>6»A
>6»A
>6»A
>6»A
>6»A
>6»A >6»A
>6»A
-46»A
@c sgst`hd elrhdnl s`rä `c sgiug`ot`;
-46»A
-46»A
-46»A
-46»A
g
x
R`hpcdzdonl vdclr`s;
R`slcvg`onl plr audcqug`r hçtlnl alolagnl;
•
HÇ^LNL ARDOJ-OGALCQLO
@c hçtlnl n` Ardoj-Ogalcslo ler`a` uo `squ`hd ghpcèagtl dct`rodtgvl qu` tg`o` uod `xdatgtun n` s`iuonl lrn`o, tdotl pdrd `c `spdagl alhl pdrd `c tg`hpl @otloa`s, cd prgh`rd n`rgvdnd t`hplrdc s` dprlxghd `o tc+4/2 plr
Cd s`iuond n`rgvdnd `o `c `spdagl pu`n` n`t`rhgodrs` `o `c puotl h`ngl prlh`ngdonl cds dprlxghdaglo`s dprlxghdagl o`s plr nge`r`oagds dc prgoagpgl (tc) y dc egodc (tc+4) n`c goar`h`otl n`c tg`hpl
Qustgtuy`onl cds `audaglo`s y `o cd `audagño y r`dirupdonl tçrhgols, s` lbtg`o`
@audagño n` Adclr `o 2 ngh`osglo`s Alosgn`r`hls uod cdhgod n`cidnd n` `sp`slr n`spr`agdbc`. Cd `audagño qu` n`sargb` sudmlrd alhplrtdhg`otl `s cd sgiug`ot`; sg iug`ot`;
@std `audagño p`rhgt` mdccdr `c vdclr n` cd ^`hp`rdturd `o audcqug`r plsgagño n` cd cdhgod y `o audcqug`r tg`hpl `o rçigh`o trdosgtlrgl.
x-t
t y -
t
k
y AE2 ^(x,Cy,t) j
t, ) y , 6 ^ ( 1 A E
y x AG ^(x,y,6) g
t, ) y , C x ( ^ > A E
x AE4 ^(x,6,t)
x-t
t y -
t
j
y
t2
k
^(g,k,j+4)
y x - y
^(g,k+4,j) t4
^(g-4,k,j) ^(g+4,k,j) tl
^(g,k,j)
x
^(g,k-4,j)
g
W cu`il r`hpcdzdhls adnd t`rhgol `o cd `audagño n` adclr bgngh`osglodc `o rçigh`o trdosgtlrgl
N` nlon` cd t`hp`rdturd qqu` u` ol alola`hls alola`hls `c cd ^(g,k,j+4)
Vdrd mdccdr cd t`hp`rdturd ^(g,k,j+4) t`o`hls; g84, k84, j86 Q` n`b` elrhdr `c sgst`hd n` `auaglo`s alo adnd g y k
EGO
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