How to specify initial conditions for a "Generic System" in the PDE App?

Question

Anna Ukolova 2017-9-14

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https://ww2.mathworks.cn/matlabcentral/answers/356737-how-to-specify-initial-conditions-for-a-generic-system-in-the-pde-app

编辑： Svetlana Pease 2017-9-29

Hello,

I'm using the PDE App (R2017a) and got a problem in defining the initial conditions. I defined a "Generic System" with a system of 2 hyperbolic PDEs.The problem is, that I've no idea how to define the initial condition within the "Solve Parameters" window for the two unknowns e.g. for u(t0). What I'm missing is an example about the necessary syntax used in the window.I should specify for u(t0) and u'(t0) functions of x and y for both unknowns u(1) and u(2).

May be you can give me an example for the correct syntax in the window?

The MATLAP Help says "The initial value can be a constant or a column vector of values on the nodes of the current mesh". How is the syntax to specify these "column vectors" to represent my functions depending on x and y??

Thanks a lot for your help!!

Anna

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Answer 1

Alan Weiss 2017-9-14

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https://ww2.mathworks.cn/matlabcentral/answers/356737-how-to-specify-initial-conditions-for-a-generic-system-in-the-pde-app#answer_281591

I believe that you should give u0 and ut0 as specified in the hyperbolic legacy solver.

Alan Weiss

MATLAB mathematical toolbox documentation

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Anna Ukolova 2017-9-15

Dear Alan,

thanks for you response! Unfortunately it doesn't work. First I've tried for u(t0) the expression

char('x.^2 + 5*cos(x.*y)','y')

and I got the error message

Then I tried as indicated in your link as an example for u'(t0) the expression

char('p(1,:).^2 + 5*cos(p(1,:).*p(2,:))','p(2,:)')

to get the nodal positions into play. But again I got an error message

So, I'm very helpless... I still does not understand, what is ment by " ...or a column vector of values on the nodes of the current mesh" and what is the MATLAB expression to achieve that!! Please help...

Thanks a lot, Anna

By the way: If I enter just constant numbers in the "char"-expressions, it's working...but I need the functions to apply the correct initial values at the nodes!

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Answer 2

Svetlana Pease 2017-9-29

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/356737-how-to-specify-initial-conditions-for-a-generic-system-in-the-pde-app#answer_283715

编辑：Svetlana Pease 2017-9-29

Dear Anna,

As a workaround, you can export the geometry from the app into the MATLAB workspace by selecting the Export Geometry Description option from the Draw menu. Then solve the problem using PDEModel.

Regards,

Svetlana Pease

Technical writer, MathWorks documentation group