Hi,
I'm trying to solve the single bubble expansion equation numerically but my plots do not seems to be quite correct.
I would appreciate any idea.
MATLAB: Single bubble expansion equation
odeode45
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You have two coupled ODEs for V_p and x. If you want to apply numerical methods (ODE15S, e.g.) for the solution, I don't see a problem.
Maybe starting at t=0 is not a good idea since powers of t appear in the denominator when you solve the first equation for xdot.
Best wishes
Torsten.
In a bubble chart you can control both the limits on the data and the limits on the (on screen) bubble sizes by using the "bubblelim" and "bubblesize" commands respectively. In the default case "bubblelim" is the range of data ([1 10] here) and "bubblesize" is the diameter units ([3 50] here). Thus the smallest bubble maps on to a marker with a diameter of 3 and the largest bubble maps on to a marker with a diameter of 50, the ratio of the largest to smallest bubble area is 50^2 / 3^2, but the ratio of the largest to smallest data unit is 10/1. The implication is that we can't make the ratio of areas from bubble 2 to bubble 1 match the ratio of areas from bubble 4 to bubble 2. Hence the difference in area between each bubble is made identical, matching the difference in data values.
In order for the bubble are ratios to match, you can set the bubble sizes to have the same ratio as the data. Because the "bubblesize" command accepts "MarkerSizes" (which refer to diameter) the inputs should include a sqrt e.g. bubblesize(sqrt([1 10])*n) where "n" is a scaling factor.
x = (1:10)';bubblechart(x,x,x);bubblesize(sqrt([1 10])*10);
Here is the documentation for "bubblesize": https://www.mathworks.com/help/releases/R2020b/matlab/ref/bubblesize.html
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