The term differential-algebraic equation was coined to comprise differential equations with
constraints (differential equations on manifolds) and singular implicit differential equations …

A review of diagonally implicit Runge-Kutta (DIRK) methods applied to rst-order ordinary di
erential equations (ODEs) is undertaken. The goal of this review is to summarize the …

Coupled Systems of Differential Algebraic and Partial Differential Equations in Circuit and
Device Simulation Page 1 Coupled Systems of Differential Algebraic and Partial Differential …

For transient eddy current problems modelled as differential-algebraic equations (DAEs), a
time integration method suitable for ordinary differential equations (ODEs) will not …

A general framework is presented for the formulation of steady-state simulation algorithms
for magnetically nonlinear eddy-current problems using implicit Runge-Kutta (RK) methods …

The stage order condition is a simplifying assumption that reduces the number of order
conditions to be fulfilled when designing a Runge–Kutta (RK) method. Because a DIRK …

Modelling electrical circuits leads to differential algebraic equations (DAEs) having a
properly stated leading term. These equations need to be solved numerically, eg in case of a …

The finite element method is a powerful tool for analyzing the magnetic characteristics of
electric machines, taking account of both complex geometry and nonlinear material …

In designing parts of Runge-Kutta methods, order conditions and truncation error coefficients
(TECs) are needed. Order conditions and TECs are typically presented as a set of trees …

Differential-algebraic equations (DAEs) are implicit singular ordinary differential equations,
which describe dynamical processes that are restricted by some constraints. In contrast to …