Laplace and inverse laplace

How to find laplace transform and inverse laplace transform of any value without using the built in functions laplace and ilaplace? please help me with the help of this one i have to use another transformation in my research work.

Answer 1

[Dev]

Hi @Maths Maths,

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.

[Maths Maths]

Thank you very much