We can find the Laplace and the Inverse Laplace transforms in MATLAB by manually applying the definitions of the same. Please find the elaboration of these definitions below-
For Laplace: Let the function be f(t) = t^2
We can use the “int” function in MATLAB to integrate and perform the Laplace, instead of using the “laplace” function. Below is a code snippet for your reference-
syms t s
f = t^2;
F = int(exp(-s*t)*f, t, 0, inf)
For Inverse Laplace: Let the function be F(s) = 1/(s^3)
We leverage the Bromwich integral to avoid the usage of the “ilaplace” function in MATLAB. Please find below a reference code snippet which performs the same-
syms s t
F = 1/s^3;
f = int(exp(s*t)*F, s, c-i*inf, c+i*inf) % Bromwich integral
For more information regarding the “int” function, please refer to the documentation link below-https://www.mathworks.com/help/releases/R2024b/symbolic/sym.int.html
I hope this helps.
