3'4 BVP Matlab 6'X

1
3.4 ??????BVP ?????? ???? ???? ?Matlab 6.X

• ?????? ????? ?? ??????? ???????????? ?? ??? ????
  ????
• ??????? ?bvp4c-solvers
• bvp4c-solvers ???? ?? ??????????? ?? ?????
  ??????? ???????????? ???? ???? ?????
• yf(x,y)
• ????? a,b ?????? ????
• bc(y(a),y(b))0

2
3.4 ?????? BVP ?????? ???? ???? ?Matlab 6.X
(????2)

• ?????? ????? ?? ??????? ???????????? ?? ??? ????
  ???? ??????? ?bvp4c-solvers
• sol bvp4c(odefun,bcfun,solinit,options)
• ????
• odefun - ?? ?? ???? ????? ???????
  ????????????
• bcfun - ?? ?? ???? ????? ???? ????
• solinit - ????????? ?? ????? ????????
• options - ?????-???? ?? ?????? ??????????
• ??????? ???????????
• sol - ????????? ?? ?????? ??????

3
3.4 ?????? BVP ?????? ???? ???? ?Matlab 6.X
(????3)

• ?????? bvpinit ? bvpval or deval ?????? ? bvp4c
  ?????? ???????? ?????? ?? ?????? ?????? ?
  sol-structure
• solinit bvpinit(x,v)
• sxint bvpval(sol,xint)
• ????
• x - ????? ?? ??????x ?? initial mesh
• v - ????? ?? guess values ?? y
• sol - ????????? ?? ???? ?? x ?y
• xint - ????? x ????? ?????? ? sol (?? bvp4c)
• sxint- ?????? ????? ? sol (?? bvp4c) ???
  ?????? xint
• ??? ?????? ?????? ?????? ??????????? ?? ????????
  bvp4c , bvpinit ? bvpval ?? ??? ????

4
3.4 ?????? BVP ?????? ???? ???? ?Matlab 6.X
(????4)

• ?????
• ?????? ?????? ??????? ???? ???? ?????
• ????? ???? ????

5
3.4 ?????? BVP ?????? ???? ???? ?Matlab 6.X
(????5)
6
3.4 ?????? BVP ?????? ???? ???? ?Matlab 6.X
(????6)

• ?????
• ?? ???? ?? ??????? ?????? ???? initial
  guess-values
• -1, 0
• ?? ???? ???? ???????

7
4. ??????? ???????????? ??????? ?????? PDE
TOOLBOX

• ????? ?????? ???? ??
• 4.1 ???????? ??????? ?? PDE TOOLBOX
• 4.2 ????? ?? ??????? ???????????? ?????? ?????
  ?????? ?PDE
• 4.3 ???? ????? ? PDE-TOOLBOX
• 4.4 ???????

8
4.1 ???????? ??????? ?? PDE TOOLBOX

• ?TOOLBOX ????? ?
• - ??????? ??????? ?? ??????? ????????????
  ??????
• ??-?????? ?? DIRICHLETNEUMANN ???? ????
• - ??????????? ????? ??????? ?? ?????
• ???? ????? ???
• ??????? ??????

9
4.2 ????? ?? ??????? ???????????? ?????? ?????
?????? ?PDE
???? ??????? ???????????? ?PDE TOOLBOX
10
4.2 ????? ?? ??????? ???????????? ?????? ?????
?????? ? PDE (????)

• ????? ?? ???? ???? ?PDE TOOLBOX

11
4.3 ???? ????? ? PDE-TOOLBOX

• ?? ???? ???? ????? (MODE) ???? ????? ?????
• draw mode
  geometry definition
• boundary condition mode specification
  of
  boundary conditions
• PDE mode
  selections of PDE
  coefficients
  that
  define the problem
• mesh mode
  finite element
  
  discretization
• solve mode
  specification of initial
  conditions and
  
  solution of the PDE
• plot mode
  post processing of the
  solution

12
4.3 ???? ????? ? PDE-TOOLBOX Draw Mode

• ????? pdetool ????? ????? - Toolbox PDE

13
4.3 ???? ????? ? PDE-TOOLBOX Draw Mode (????)

• ???? ???? ????? ?????? ???? ??-????? ?2U0
• ???? ???? 1x3 (??-????)
• ?Options ?????? ?Grid, Snap ???? ?? ?
• Axes Limits ??????? ?????? ????

14
4.3 ???? ????? ? PDE-TOOLBOX Draw Mode (????2)

• ?Draw ?????? rectangle/square , ????? ????
  ??????? ?? ???? ?????? 3,1 ?? ????? 0,0

???????????
15
4.3 ???? ????? ? PDE-TOOLBOX Draw Mode (????4)

• ???? ????? ????? ???? ???? ??????? ???? Object
  Dialog ???? ????? ????????????

16
4.3 ???? ????? ? PDE-TOOLBOXBoundary Condition
Mode (????5)

• ?Boundary ?????? Boundary Mode ?Show Edge
  Labels

• ???? ???? ????? ???? ?????
• Boundary conditions
• ?????? ???? Dirichlet
• ??????? h1 ?r-1 ????
• ?????? ??? 4 ?2 ?h1
• ?r1 ??????? 1 ?3

17
4.3 ???? ????? ? PDE-TOOLBOXPDE Mode (????6)

• ?????? ?????? PDE , PDE mode ?PDE Specifications
  
• ?????? elliptic ???????? ?? ?????????????
  ???????

18
4.3 ???? ????? ? PDE-TOOLBOX Mesh Mode (????7)

• ?????? ?Mesh ? ?Mesh Mode ?????? ?Initialize Mesh
• ????? ????? ?????? ??? ????? ????

19
4.3 ???? ????? ? PDE-TOOLBOX Solve Mode (????8)

• ?SOLVE ?????? Solve PDE ??????? ????? ?? ??????

20
4.3 ???? ????? ? PDE-TOOLBOX Plot Mode (????9)

• ?Plot ?????? Parameters ??????? ???? Plot
  Selection
• ?????? ???? color, contour,Height(3-D plot)

21
4.3 ???? ????? ? PDE-TOOLBOX Plot Mode (????10)

• ???? ???????

22
4.3 ?????? ????? ??????

• ?????? ??????? ???? ????? ??? ?? ?????? ?Solve gt
  Export Solution
• ????? u - ???? ?????? ???? ????? ?????
• ???? ????? ???? ????? ?Mesh Mode gt Show Node
  Labels

u u 0 -0.3881
23
4.3 ????? ??????

• ??? ????? ?? ?????? ???? ?Mypdesample.m ????
  ?File ????? Save as ???? ??

24
4.4 ???????

• ???? ??????? ???? ?????? ????? ???? ???? ????
• sin(py2) ??????? 4,2
• -0.5x4(3-x)2 ????? 1
• ?-0.5x2(3-x)4 ????? 3
• ???? ???? ??????? ??????? Boundary Condition
• ???? ??? ????? ??? ????? height
• ??? ????? ???? ???? ?? ?????? ??????? (??? ????)
  ????? ???? ?????? ?????
• ?????
• ????? ?grid ?? ?????? 0.1, ????? ??????? 0.2,
  ????? ???? ??????? ??????? ????? ????? ???? ?????
  ??????
• ?Draw Mode ????? ????? Set Formula
• R1-(R2R3R4R5)C1C2C3C4
• ?Boundary Mode ????? ?Remove All Subdomain
  Orders

25
4.4 ??????? (????)

• ????? ??? ????? ?????? ?? ???? ??????

26
4.4 ??????? (????2)

• ????? ??? ????? ?????? ?? ???? ?????? (????)

27
4.4 ??????? (????3)

• ????? ??? ????? ?????? ?? ???? ?????? (????2)
• ?Boundary Mode ????? ?
• Remove All Subdomain Orders