Galpern-Sobolev type equations with non-constant coefficients

We study Galpern-Sobolev equations by the help of a quaternionic operator calculus. Some previous work will be extended to the case of variable coefficients. Rothe's time discretization method is used to reduce the problem to a series of stationary problems. Solving the resulting stationary problems by means of quaternionic analysis we obtain integral representation formulas for the solution of the Galpern-Sobolev equation. The truncation error and the stability of the method is studied, too.