This set of functions allows a user to numerically approximate an inverse Laplace transform for any function of "s". The function to convert can be passed in as an argument, along with the desired times at which the function should be evaluated. The output is the response of the system at the requested times.
For instance, consider a ramp function.
f = @(s) 2/s^2;
t = [1 2 3 4 5]';
talbot_inversion(f, t)
The time response output is [2 4 6 8 10], as expected.
These methods can be used on problems of considerably more difficulty as well and are intended to approximate an inverse Laplace transform where an exact solution is unknown.
Two basic solvers (Euler and Talbot) are included, along with *symbolic* versions of those solvers. The symbolic solutions take substantially longer to calculate, but are capable of any desired accuracy. Also, the symbolic versions require the Symbolic Toolbox, whereas the basic versions do not.
Please see example_inversions.pdf or html/example_inversions.html to get started! |