Semi-implicit Euler schemes for ordinary differential inclusions

TL;DR

This paper introduces and analyzes two semi-implicit Euler schemes for differential inclusions, demonstrating improved stability, robustness, and computational efficiency over traditional implicit Euler methods.

Contribution

The paper proposes two semi-implicit Euler schemes for differential inclusions, providing detailed error analysis and showing advantages over implicit schemes in stability and robustness.

Findings

Semi-implicit schemes inherit favorable stability properties.

Performance surpasses implicit Euler scheme in efficiency.

Schemes are more robust to spatial discretization.

Abstract

Two semi-implicit Euler schemes for differential inclusions are proposed and analyzed in depth. An error analysis shows that both semi-implicit schemes inherit favorable stability properties from the differential inclusion. Their performance is considerably better than that of the implicit Euler scheme, because instead of implicit inclusions only implicit equations have to be solved for computing their images. In addition, they are more robust with respect to spatial discretization than the implicit Euler scheme.