An example of using CUDA technology for the numerical solution of the Fredholm integral equation of the second kind:
The integral is approximated by a compound quadrature formula of order m:
(For the rectangle and trapezoidal rule m is equals 2 and for Simpson's rule m is equals 4.) After substituting this formula into the integral equation and neglecting the small error of the quadrature formula, for each partition point of the segment [a,b] we obtain a linear equation:
Finally, solving this system, we obtain an approximation for the desired function by the formula:
The mesh convergence is estimated by the relation:
where the integral in the norm of the L2 space is calculated using adaptive quadrature.
CUDA, cuBLAS, cuSOLVER, gnuplot