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The paper proposes an efficient and insightful approach for solving neutral delay differential equations (NDDE) with high-frequency inputs. This paper aims to overcome the need to use a very small time step when high frequencies are present. High-frequency signals abound in communication circuits when modulated signals are involved.

The method involves an asymptotic expansion of the solution and each term in the expansion can be determined either from NDDE without oscillatory inputs or recursive equations. Such an approach leads to an efficient algorithm with a performance that improves as the input frequency increases.

An example shall indicate the salient features of the method. Its improved performance shall be shown when the input frequency increases. The example is chosen as it is similar to that in literature concerned with partial element equivalent circuit (PEEC) circuits (Bellen et al., 1999). Its structure shall also be shown to enable insights into the behaviour of the system governed by the differential equation.

The method is novel in its application to NDDE as arises in engineering applications such as those involving PEEC circuits. In addition, the focus of the method is on a technique suitable for high-frequency signals.

The purpose of the paper is the simulation of nonuniform transmission lines.

The method involves a Magnus expansion and a numerical Laplace transform. The method involves a judicious arrangement of the governing equations so as to enable efficient simulation.

The results confirm an effective and efficient numerical solver for inclusion of nonuniform transmission lines in circuit simulation.

The work combines a Magnus expansion and numerical Laplace transform algorithm in a novel manner and applies the resultant algorithm for the effective and efficient simulation of nonuniform transmission lines.

The paper is concerned with interpolatory proper orthogonal decomposition (IPOD) methods for nonlinear transmission line circuits. This paper aims to examine several factors that must be considered when applying such model reduction techniques to this kind of circuit.

Two types of POD will be implemented. In each case, the choice of the order of the reduced model and the order of the interpolation space shall be considered. The stability of the models shall be explored.

The results indicate that the order for the reduced model to obtain accurate results depends on the chosen method when considering nonlinear transmission lines. The results also indicate that the structure of the nonlinear transmission line is crucial for determining the stability of the reduced models.

The work compares two IPOD methods and discusses the issues involved in achieving an accurate and stable reduced-order model for a nonlinear transmission line.

This paper aims to explore a new approach for time-domain modelling of interconnects with highly oscillatory modulated sources.

The paper uses an asymptotic method in conjunction with the Green’s function of the telegrapher’s equations. The Green’s function is expressed as a series of rational functions in the Laplace domain and are converted to pole-residue form, thereby enabling time-domain implementation.

The results indicate that the method is accurate for modelling interconnects when wide-varying frequencies are present in the sources.

The technique is important in circuit design for assessing signal integrity and in electromagnetic compatibility testing.

The paper is aimed at the development of novel model reduction techniques for nonlinear systems.

The analysis is based on the bilinear and polynomial representation of nonlinear systems and the exact solution of the bilinear system in terms of Volterra series. Two sets of Krylov subspaces are identified which capture the most essential part of the input‐output behaviour of the system.

The paper proposes two novel model‐reduction strategies for nonlinear systems. The first involves the development, in a novel manner compared with previous approaches, of a reduced‐order model from a bilinear representation of the system, while the second involves reducing a polynomial approximation using Krylov subspaces derived from a related bilinear representation. Both techniques are shown to be effective through the evidence of a standard test example.

The proposed methodology is applicable to so‐called weakly nonlinear systems, where both the bilinear and polynomial representations are valid.

The suggested methods lead to an improvement in the accuracy of nonlinear model reduction, which is of paramount importance for the efficient simulation of state‐of‐the‐art dynamical systems arising in all aspects of engineering.

The proposed novel approaches for model reduction are particularly beneficial for the design of controllers for nonlinear systems and for the design and analysis of radio‐frequency integrated circuits.

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 in electronic systems subject to modulated signals.

The paper combines a Filon‐type method with waveform relaxation techniques for nonlinear systems of ODEs.

The analysis includes numerical examples to compare with traditional methods such as the trapezoidal rule and Runge‐Kutta methods. This comparison shows that the proposed approach can be very effective when dealing with systems of highly oscillatory differential equations.

The present paper constitutes a preliminary study of Filon‐type methods applied to highly oscillatory ODEs in the context of electronic systems, and it is a starting point for future research that will address more general cases.

The proposed method makes use of novel and recent techniques in the area of highly oscillatory problems, and it proves to be particularly useful in cases where standard methods become expensive to implement.

The paper aims to propose several new approaches for the discrete‐time integration of stiff non‐linear differential equations.

The proposed approaches build on a method developed by the authors involving Padé approximates about each function sample. Both single‐ and multi‐step methods are suggested. The use of Richardson extrapolation is recommended for increasing efficiency.

The efficacy of the methods is shown using two examples and results are compared to a standard integration technique.

The paper shows that the methods are suitable for application in any field of science requiring efficient and accurate numerical solution of stiff differential equations.

The purpose of this paper is to investigate limit cycles in digitally Proportional, Integral and Derivative (PID) controlled buck regulators. Filtering is examined as a means of removing the limit cycles in digitally controlled buck regulators.

The paper explains why limit cycles occur in a digitally PID controlled buck converter. It then proceeds to propose two filters for their elimination. Results indicate the effectiveness of each of the filters.

The paper gives a mathematical analysis of the occurrence of limit cycles in digitally controlled PID buck regulators. It finds that notch and comb filters are effective for the purpose of eliminating limit cycles in buck regulators.

The paper employs a model of the buck regulator inclusive of the inductor loss – this was not done to date for this type of work. The paper analyses PID control. This was not done in the manner given. The paper addresses filtering as a means of removing limit cycles. It examines the effect of changing the digital controller parameters on the requirements of the filters.

The purpose of this paper is to propose a methodology for forming compact reduced‐order macromodels of interconnect systems to enable real‐time design exploration and efficient manufacturing tolerance assessment.

A multi‐parameter moment‐matching‐based technique and a multivariate orthonormal macromodelling technique are combined to form an effective and efficient reduced‐order model that approximates the frequency‐domain behaviour of an interconnect system based on several design variables.

Results will confirm the efficacy of the approach and its superiority to application of the moment‐matching‐based method alone.

With the ever growing complexity of high‐frequency systems in the electronic industry, formation of compact macromodels is crucial for fast and efficient design and analysis.

Combination of the individual techniques is novel and increases the efficiency of the ultimate macromodel.

This paper presents the application in circuit simulation of a method for model reduction of nonlinear systems that has recently been developed for chemical systems. The technique is an extension of the well‐known balanced truncation method that has been applied extensively in the reduction of linear systems. The technique involves the formation of controllability and observability gramians either by simulated results or by measurement data. The empirical gramians are subsequently employed to determine a subspace of the full state‐space that contains the most significant dynamics of the system. A Galerkin projection is used to project the system onto the subspace to form a lower‐dimensional nonlinear model. The method is applied to a nonlinear resistor network which is a standard example for exemplifying the effectiveness of a nonlinear reduction strategy.