How can I solve PDE with boundary condition?

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Riyadh Muttaleb
Riyadh Muttaleb 2017-8-17
评论： Riyadh Muttaleb 2017-8-30
Hi All, I do have Ws dC/dz + Kc d2C/dz2 - X=0 where Ws and X are constant Z from (0 to 5 step 0.5) and I do have Kc values each 0.5 m,
How can I solve this PDE with Matlab, using B.C. (C at 0= 10) and (C at 5 =0)
Thanks in advance
Riyadh
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Kuifeng
Kuifeng 2017-8-18
Example answer, Ref to Chap 5, Part 5.2 Steady 1D Convection and diffusion of 'An introduction to computational fluid dynamics 2nd edition' by Versteeg and Malalasekera

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回答（2 个）

Torsten
Torsten 2017-8-18
Use "bvp4c".
By the way: this is a second-order ODE, not a PDE.
Best wishes
Torsten.
Precise Simulation
Precise Simulation 2017-8-24
Alternatively, if you still prefer to solve it as a PDE, you can quite easily input and solve it with the FEATool Multiphysics FEM Finite Element toolbox directly in Matlab. The small m-script below shows how this can be achieved
% FEATool FEA problem definition.
fea.sdim = {'z'}; % Space coordinate/dimension name.
fea.dvar = {'C'}; % Dependent variable name.
fea.sfun = {'sflag1'}; % 1st order P1 FEM shape function.
s_eqn = 'Ws*Cz + Kc*Cz_z - X = 0'; % String equation definition.
fea.eqn = parseeqn( s_eqn, fea.dvar, fea.sdim );
fea.grid = linegrid( 10, 0, 5 ); % Line grid/mesh.
fea.coef = { 'Ws' 1; 'Kc' '2*z'; 'X' '3' }; % Equation coefficents/expressions.
fea.bdr.d = {10 0}; % Dirichlet BCs.
fea.bdr.n = {[] []}; % (Optional) Neumann BCs.
% Check, parse, and solve FEA problem.
fea = parseprob( fea );
fea.sol.u = solvestat( fea );
% Postprocess and visualize solution.
postplot( fea, 'surfexpr', 'C' )
  1 个评论
Riyadh Muttaleb
Riyadh Muttaleb 2017-8-30
Sorry for late response, In was in small vacation, I tried to implement the m-script, but an error says that "Undefined function or variable 'parseeqn'"
Thank you,

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