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Persamaan Diferensial Parsial
[Partial Dierential Equation (PDE)]
Joko Wintoko
Kuliah Matematika TeknikKimia 2
JTK/T/!"M/2#$$
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The %eat &on'utionEquation
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The %eat &on'utionEquation
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EXPLICIT METHOD
Paraoli PDEs
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D*+ e,-liit
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D*+ e,-liit
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E,am-le $
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E,am-le $. ont'
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E,am-le $. ont'
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&on0er1ene an' tailit3
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Prolem 4ith e,-liitmetho'
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IMPLICIT METHOD
Paraoli PDEs
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5m-liit 0s E,-liit Metho's
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D*+ im-liit
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D*+ im-liit
r the frst interior node (i=1):
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D*+ im-liit
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E,am-le 2
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E,am-le 2. ont'
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E,am-le 2. ont'
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CRAN!NICOL"ONMETHOD
Paraoli PDEs
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* om-utational moleule for the&rank67iolson metho'
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D*+ &rank67iolson
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D*+ &rank67iolson
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E,am-le 8
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E,am-le 8. ont'
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&om-arison of anal3tial an'
numerial solutions
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PARA#OLIC E$%ATION INT&O "PATIALDIMEN"ION"
Paraoli PDEs
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Paraoli equation in t4o s-atial
'imensions
E'i*it:
+i*it:Co+,t-tion- +ethod is -s in re.io,s se*tions/Loss the tridi-0on- +-tri' or+Co+,t-tion- ti+e 22
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Paraoli equation in t4o s-atial
'imensions
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Paraoli equation in t4o s-atial 'imensionsADI (-tern-tin0!dire*tion i+i*it) "*he+e
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*D5 (alternatin16'iretion im-liit)
heme
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*D5 (alternatin16'iretion im-liit)
heme
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E,am-le 9
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E,am-le 9 ont'
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E,am-le 9 ont'
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E,am-le 9 ont'
