The invariant imbedding numerical method for Fredholm integral equations with degenerate kernels

AbstractConsider the Fredholm integral equation u(t, x)=f(t)+∫0xk(t, y)u(y, x)dy, 0 ⩽ t ⩽ x, where the kernel k has the form k(t,y)=∑i=1Mgi(t)hi(y) 0⩽t, y. A Cauchy problem equivalent to the original integral equation is derived and validated. A general Fortran program has been written, and numerical results are displayed. Emphasis is on the inhomogeneous problem, though some remarks about the eigenvalue problem are given