, I need help! I do not get to have the graph of the solution of a differential equation.

2 次查看（过去 30 天）

显示更早的评论

Nadjah 2015-1-2

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/168735-i-need-help-i-do-not-get-to-have-the-graph-of-the-solution-of-a-differential-equation

回答： Andres Bayona 2019-4-25

采纳的回答： Roger Stafford

I have a differential equation of the first order. It describes the basic velocity profile of fluid flowing over an inclined plane.
I used the Euler method with Matlab to solve the equation.
My goal is to plot the graph of the solution of this equation. I want to have the velocity U on axis (ox) on the interval [0,18], in fonction of the height of the flow channel y, on axis (oy) in the interval [0,200] .
No errors in the program are displayed, but the result I get is different from that of the article on which I work. The velocity profile should be parabolic while I get a straight line!
I Attach the program that I do, the graph that I get and the graph that I must have.Could you please help me understand and solve the problem? I will be very grateful.

1 个评论
显示 -1更早的评论隐藏 -1更早的评论

Nadjah 2015-1-2

Sorry, I think I have not attached the graphs! Thank you.

请先登录，再进行评论。

请先登录，再回答此问题。

采纳的回答

Roger Stafford 2015-1-2

2
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/168735-i-need-help-i-do-not-get-to-have-the-graph-of-the-solution-of-a-differential-equation#answer_163858

在 MATLAB Online 中打开

I am guessing that you left out the parentheses in the denominator of F, which would presumably be this instead:

   F=@(x,s)(2-(x./100))./(1+sqrt(1+0.003*x.^2.*(1-exp(-x./25)).^2.*(200-x)./50));
                         ^                                                     ^

The values for U I get with this alteration do not agree with those in your 'profile vitesse.pdf' plot but the shape appears to be similar to that plot.

Also I find it curious that F, as you have defined it, does not depend on the second argument 's', so you are simply finding U(x) = the integral of F(t) from t = 0 to x where F does not depend on U. In other words, it is not really a differential equation but merely an integral which could have been solved using 'cumtrapz'.

8 个评论
显示 6更早的评论隐藏 6更早的评论

Roger Stafford 2015-1-5

Not quite identical. There is the discrepancy between U being 16.2473 with matlab and somewhere near 15.3 for the article for x = 200.

Nadjah 2015-1-6

The basic velosity profile for L=200.pdf

Hello; The graph '' profile vitesse.pdf '' is the one I got with Maple and that I found (before to solve the problem with Matlab)) close to that of the article (herewith the graph of the article). Whilst if we correct the term in denominator: F=@(x,s)(2-(x./100))./(1+sqrt(1+0.003*x.^2.*(1-exp(-x./25)).^2.* (200-x)./50) ) which becomes: F=@(x,s)(2-(x./100))./(1+sqrt(1+0.003*x.^2.*(1-exp(-x./25)).^2.*(200-x))) you will notice that the result of Matlab is much better! Thank you.

请先登录，再进行评论。