evaluating double integral iteratively

I am trying to discretize a kernel K(x,t) for solving an integral equation. I need to implement

for i=1...N
   for j=1..N
     a(i,j) = Int1 Int2 K(x,t)dx dt

where Int1 has limits i/N to (i+1)/N and Int2 has limits j/N to (j+1)/N

I tried the symbolic computation but it takes a lot of time. I want to use the numerical computation and speed it up. thanks

Answer 1

[Star Strider]

If K(x,t) is a function, you can use integral2.

[R yan]

thanks. Does integral2 implement the iterative version?? I mean in Int1 Int2 K(x,t)dxdt, does it evaluate the integral Int2 K(x,t)dx treating t as constant?? and then evaluate Int1 over t.

[Star Strider]

My pleasure!

That’s my understanding of how integral2 works. See the More About in the documentation, and its friends (linked to at the end of the page). Note that only integral can take array-valued functions, so if K(x,t) in one such, you’ll have to nest calls to integral. If it’s scalar-valued, the integral functions will be happy and will return a scalar.