On numerical methods for highly oscillatory problems in circuit simulation

Abstract

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 in electronic systems subject to modulated signals.

Design/methodology/approach

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

Findings

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.

Research limitations/implications

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.

Originality/value

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.

Citation

Condon, M., Deaño, A., Iserles, A., Maczyński, K. and Xu, T. (2009), "On numerical methods for highly oscillatory problems in circuit simulation", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 28 No. 6, pp. 1607-1618. https://doi.org/10.1108/03321640910999897