Generalized convolution quadrature with variable time stepping (Q2856616)

In order to solve linear parabolic and hyperbolic evolution equations, the authors present a generalized convolution quadrature which allows for variable time stepping and develop a new theory for its error analysis. Ones use a low-order implicit Euler method for the time discretization which is justified for problems where the solution contains nonuniformly distributed irregularities. Adaptivity in the time integration of the scalar ordinary differential equations \(y^{\prime }=zy+g\) is used. The theory is applied to the space-time discretization of the retarded potential integral equations which arise if the wave equation in an unbounded exterior domain is formulated as a space-time integral equation on the boundary of the scatterer.