BACKWARD EULER METHOD AS A POSITIVITY PRESERVING METHOD FOR ABSTRACT INTEGRAL EQUATIONS OF CONVOLUTION TYPE

It is shown that the backward Euler approximation to the solution of a wide class of linear, homogeneous equations with memory can be expressed as an average of the solution itself. This result implies that the numerical solution inherits some qualitative properties of the exact solution, such as positivity and contractivity. Numerical experiments, showing that neither the telegraph nor the fractional diffusion-wave two-dimensional equations preserve positivity, are provided.