... differential equations. Applying the separation of variables method analytical solutions are obtained for an infinitely long conducting cylindrical segment in transient magnetic field. A special case for such a configuration is an infinitely long cylinder with longitudinal crack. The analytical solutions...

.... Applying a generalized Schur complement to the differential algebraic equation system yields an ordinary differential equation (ODE) system. This ODE system can be integrated in time using explicit time integration schemes by which the solution of high-dimensional nonlinear algebraic systems of equations...

... as the step size is governed by the highest frequency present in the signal. Several approaches have been proposed to deal with such cases including envelope simulation tools such as Pedro and Carvalho (2002) , multirate partial differential equation methods such as Roychowdhury (2001) and multiscale...

... parts. The former is expressed by a nonlinear differential equation. The goal of this paper was to obtain a closed form of the solution to one of the most popular nonlinear differential equations used for the AC electric arc modelling. Design/methodology/approach The solution has been obtained...

...Ivan Yatchev; Rumena Stancheva; Iliana Marinova; Domenico Lahaye; Wouter Mulckhuyse Purpose The purpose of this paper is to provide a framework for the implementation of an adjoint sensitivity formulation for least‐squares partial differential equations constrained optimization problems exploiting...

... Group Publishing Limited 2011 Eddy currents Differential equations Gauging Schur complement method Preconditioned conjugate gradients Already for several years transient simulation of the magnetoquasistatic (MQS) field is an established technique (Tsukerman et al., 1993...

...Ludger Klinkenbusch; Wolfgang Mathis; J.C. Chedjou; K. Kyamakya Purpose This paper seeks to develop, propose and validate, through a series of presentable examples, a comprehensive high‐precision and ultra‐fast computing concept for solving stiff ordinary differential equations (ODEs) and partial...

... the geometrical information of the coordinate system chosen (charts), and the underlying features of the geometry associated to Maxwell differential equations, as we are going to show in detail. The important thing that we remark is that we introduce in these equations two parameters (permittivity...

... Wave propagation Differential equations Nowadays, a variety of methods exist for the numerical treatment of the time‐domain Maxwell equations, ranging from the well‐established and still prominent finite difference time‐domain (FDTD) methods based on Yee's scheme (Yee, 1966 ; Taflove...

...Bo Hu Li; Tianyuan Xiao; Lin Zhang; Marissa Condon; Alfredo Deaño; Arieh Iserles; Kornel Maczyński; Tao Xu Purpose The purpose of this paper is to analyse a novel technique for an efficient numerical approximation of systems of highly oscillatory ordinary differential equations (ODEs) that arise...

... collocation method will be used to solve the governing differential equations of the problem. This method uses trial functions that satisfy, in a certain region the governing differential equations. Complete sets of solutions of such equations are required so that completeness and convergence can...

...Mauro Feliziani; Alessandro Salvini; Alessandro Toscano; Lucio Vegni; Marissa Condon; Emira Dautbegovic; Tao Xu Purpose The paper aims to propose several new approaches for the discrete‐time integration of stiff non‐linear differential equations. Design/methodology/approach The proposed...

... analysis Differential equations The discretization of partial differential equations by means of finite elements leads to the resolution of one or several sparse linear systems of equations. When these linear systems of equations are solved by iterative methods, preconditioning techniques...

... such as the Helmholtz free energy or the Gibbs' free energy. Refer Maugin (1999) and Ikeda (1990) for more details. Finite element analysis Differential equations Electromechanical devices While electrical engineers often focus on the electrical aspects of engineering problems, many real‐life...

.... This paper discusses a flaw of frequently used standard elements in boundary‐element‐method and shows a way to avoid it. © Emerald Group Publishing Limited 2004 Boundary‐elements methods Differential equations Numerical analysis Theoretically constant‐linear mixed elements are able...