ilaplace - Inverse Laplace transform

Syntax

Description

F = ilaplace(L) computes the inverse Laplace transform of the symbolic expression L. This syntax assumes that L is a function of the variable s, and the returned value F is a function of t.

If L = L(t), ilaplace returns a function of x.

F = F(x)

By definition, the inverse Laplace transform is

where c is a real number selected so that all singularities of L(s) are to the left of the line s = c, i.

F = ilaplace(L,y) computes the inverse Laplace transform F as a function of y instead of the default variable t.

F = ilaplace(L,y,x) computes the inverse Laplace transform and lets you specify that F is a function of x and L is a function of y.

Examples

syms s
f = 1/s^2;
ilaplace(f)

ans =
t

syms a t
g = 1/(t-a)^2;
ilaplace(g)

ans =
x*exp(a*x)

syms x u
syms a real
f = 1/(u^2-a^2);
simplify(ilaplace(f,x))

ans =
sinh(a*x)/a

See Also

ifourier | iztrans | laplace

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