Implementing a first order forward difference scheme in MATLAB
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Hi everyone,
I am trying to solve the first order differential equation on the figure below:
So that I can reproduce the curves below:
As you can see from the curves the specific heat has only two values 1.66 and 1.4. In the X equation, all the variables except x are constant. x can be taken to increase from 0 to 10. I want to produce the variation of M with X. Here they used first order forward difference, I'd like to know how I could do this using MATLAB. I'd appreciate any form of assistance. Regards Charles
1 个评论
Lukas Bystricky
2015-7-28
编辑：Lukas Bystricky
2015-7-28
Alternatively, if you're interested in replicating that graph exactly (using first order methods), you should look up the forward euler method. It's very simple and requires little more than a single for loop.
采纳的回答
fun=@(X,M)(((2+(gamma-1)*M^2)/2)^(-1/(gamma-1)))/((M-1)*(2+(gamma-1)*M)/(2+(gamma-1)*M^2));
gamma=1.4;
[X1,M1]=ode45(fun,[0 10],1.001);
gamma=1.66;
[X2,M2]=ode45(fun,[0 10],1.001];
plot(X1,M1(:,1),X2,M2(:,1));
Best wishes
Torsten.
8 个评论
Charles Kubeka
2015-7-28
编辑：Charles Kubeka
2015-7-28
Thanks for the quick response guys Torsten I tried to run your script and I got the following error: Error: Unbalanced or unexpected parenthesis or bracket. I fixed that as follows:
gamma=1.4; fun=@(X,M)((2+(gamma-1)*M^2/2)^(-1/(gamma-1)))/((M-1)*(2+(gamma-1)*M)/(2+(gamma-1)*M^2)); [X1,M1]=ode45(fun,[0 10],0); gamma=1.66; [X2,M2]=ode45(fun,[0 10],0); plot(X1,M1(:,1),X2,M2(:,1));
But now I get this:
The form of the curve looks different from what they got in the figure. I Appreciate your assistance.
Torsten
2015-7-28
Should be corrected, but better check again.
Best wishes
Torsten.
Lukas Bystricky
2015-7-28
The brackets are a little incorrect:
(2+(gamma-1)*M^2/2)
should be
((2+(gamma-1)*M^2)/2)
for instance.
Torsten
2015-7-28
I changed the code ; the initial condition is M(X=0)=1 instead of M(X=0)=0.
Best wishes
Torsten.
Charles Kubeka
2015-7-28
I made some corrections in the brackets now I get this:
The curve seems like a mirror of the original. The M values are supposed to be positive. Thanks again.
Lukas Bystricky
2015-7-28
You didn't change the initial condition. M(0) = 1 (or thereabouts) from the original graph.
Torsten
2015-7-28
You took the code from above with the change in the initial condition for M ?
Best wishes
Torsten.
Charles Kubeka
2015-7-28
编辑：Charles Kubeka
2015-7-28
I just did and now I get this:
This is much much better, thanks a lot guys. Do you have an idea why the other curve is not showing or are they identical? Also how can I extract the values of M for each X value?
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