Numerical solution of ODEs involving the derivative of a Preisach operator and with discontinuous RHS

Abstract

The purpose of this paper is to numerically solve a special class of ordinary differential equations with discontinuities on the right-hand side and with the Preisach operator under the derivative. We present an algorithm that we devised to numerically integrate this equation making use of a specific approximation from our companion paper, which provided an approximate solution where singularities were expected to occur. We found when the discontinuities forced the right-hand side closer to zero, that the graph of the solution had more parabolic-like curvature similar to the graphs of the solutions using our approximation.