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Loop possible? [Blasius Equation with fsolve]

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MaxPr on 11 Aug 2016
Commented: MaxPr on 11 Aug 2016
Hey ! So im pretty new to matlab, but I'm working my way into it. So now I have come across a problem, I'm not sure how to solve: I want to solve the blasius equation for a moving plate, thus different BC's than some might recognise ( f''' + 1/2ff''=0, with BC's: f(0)=0, f'(0)=1 and f'(inf)=0. I know it's very easy to solve with the ODE (+shooting method) or rather the BVP command, but I need this example to apply it to a little more complex model, so I will need to do this with finite-differences(something similar to the keller box method). So since this will be boiling down to a problem formulation of a system of nonlinear equations, I figured why not use fsolve? I figured I would program a function containing all my BC's and equations, so I can just make a grid off "nodes" which will solve the equations at the corresponding node. However I seem to be stuck and or just stupid:
%%Keller box Basius with fSolve
deltaEta=0.1; %stepsize
N=(etaInf-eta0)/deltaEta; %number of nodes
f=zeroes(N,1);g=ones(N,1);h=zeros(N,1); %freeing up space
%%call solver
Sol = fsolve(blasiuskeller2(f,g,h,N,deltaEta), anfangswert);
plot(eta0:edltaEta:etaInf, fval2);
%%equations mit discretiszation
function fval = blasiuskeller2(f,g,h,N,deltaEta)
% freeing up space
% Define functions as F(X)=0
for i=1:N-1
fval1(i)=(f(i+1)-f(i))/deltaEta - (g(i+1)+g(i))/2;
fval2(i)=(g(i+1)-g(i))/deltaEta - (h(i+1)+h(i))/2;
fval3(i)=(h(i+1)-h(i))/deltaEta + (1/8)*(f(i+1)+f(i))*(h(i+1)+h(i));
fval(:,1)=[f(1);g(1);fval2(1)]; %initial value
for i=2:(N-1)
fval(:,N)=[fval1(N-1);1-g(N);fval2(N-1)]; %Boundary value
Pretty sure this is possible, but not sure if I'm on the right track here. Any help would be greatly appreciated!

Accepted Answer

Torsten on 11 Aug 2016
Edited: Torsten on 11 Aug 2016
I did not check your equations, but already your call to fsolve is incorrect:
sol = fsolve(@(x)blasiuskeller2(x(1:N),x(N+1:2*N),x(2*N+1:3*N),N,deltaEta), anfangswert);
Best wishes

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