function on separate interval

Question

Oluwaseun Lijoka 2016-3-25

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评论： Oluwaseun Lijoka 2016-3-26

Hello there, I have a function f(x,t) defined on (0,1). The function is however discontinuous at x=1/2 such that we have two separate values f1(x,t) for x in (0,1/2) and f2(x,t) for x in (1/2, 1). How do I program this function with M function file that takes input x and t?. Arbitrary function can be used to explain. Thanks a lot

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Walter Roberson 2016-3-25

Is x a scalar or a vector?

Oluwaseun Lijoka 2016-3-26

x is allowed to be a vector. Mostly computed via quadrature.@Robertson

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Answer 1

Ced 2016-3-25

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编辑：Ced 2016-3-25

在 MATLAB Online 中打开

This means that you have defined a function with an output (in your case the variable f), but have not assigned it. This would happen if x does not fall into any of your cases.

Your if conditions are a bit strange.

(x<=1/2) will return 0 if false, 1 if true. So, if e.g. x = 0, then x(x<=1/2) = x(1) = 0, which is considered false instead of true.

This should work better:

function f = exact_soln(x,t,c_1,c_2)
fn=@(x)sin(2*pi*x);
if x <= 0.5 % domain section 1
    f= 0.5*(fn(x+c_1*t) + fn(x-c_1*t));
else % domain section 2, 0.5 < x
    f= 0.5*(fn(x+c_2*t) + fn(x-c_2*t));
end
end

Having an else statement ensures that no matter x, f will always get a value.

Note that the boundaries x == 0 and x == 1 are actually not checked! If you need your wave to stop there, you could either add more if/else statements, or simply bound x before hand, i.e.

x = max(min(x,1),0);

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Oluwaseun Lijoka 2016-3-25

Thanks Ced, I actually extended the solution by f=0 elsewhere before but your idea is simple and better. I also like the idea of bounding x as well. Thanks a lot.

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