A stable, accurate method of numerical integration for nonlinear systems

Abstract

A bstract-A namerid integntim scheme is presented which 1) is stable forstnble,linearsystensrad2)hs3eerm~vPriesasT4forlinearand nonlinear systems.

Efficient higher order implicit one-step methods for integration of stiff differential equations

“…(28) can be seen as a refinement of the trapezoidal rule and bears a close relation to the formula developed by Calahan [5]. For all presented formulas except (27), it turns out that ~ (h2) equals a diagonal Pad6 approximant for e hz with an order at least equal to the order of the integration formula.…”

Modelling and Discretization of Circuit Problems

“…As a more flexible and universal approach a charge/flux-oriented formulation can be taken for energy storing elements which reflects better the underlying physics of the circuit devices, see e. g. Calahan [31], Chua and Lin [38], Ward and Dutton [253]. It requires the inclusion of terminal charges q and branch fluxes φ into the set of network variables.…”

Improved Transient Simulation of Salient-Pole Synchronous Generators With Internal and Ground Faults in the Stator Winding

“…The semi-implicit Calahan method [18] is chosen to solve the state equations. Iteration is not needed in the calculation due to the explicit recursive relation.…”

“…Moreover, its computing speed and stability are better than for the fourth-order Runga-Kutta method. is the calculation time step, , [18]. By adopting a nonzero transition resistance, albeit very small, to simulate either a solid ground fault or an internal short-circuit fault, the Calahan method ensures good stability toward a solution.…”