On the numerical solution of integral equations with piecewise continuous displacement kernels (Q804277)

The authors give the solution of the equation \(x(t)-\int^{T}_{0}k(t- r)x(r)dr=f(t),\) \(0\leq t\leq T\), where k(t) is a piecewise continuous \(p\times p\) matrix valued kernel and f(t) is a piecewise continuous p vector valued function, and prove that it is equivalent to the solution of an initial value problem for a partial differential equation. A difference scheme for the last problem is derived and compared with a corresponding quadrature method.