Publication

Emergence of complexity in a frictional system: reproducing earthquake statistics

2026

Abstract

This report presents a numerical study of the Burridge-Knopoff (BK) springslider model applied to earthquake fault mechanics, following the non-dimensional formulation of Erickson et al. (2011). Rate-and-state friction couples N sliding blocks, and a single dimensionless parameter ε controls a transition from stable sliding through periodic stick-slip and quasi-periodicity to deterministic chaos. Four integration methods are compared as a function of system stiffness: explicit Euler, symplectic Velocity Verlet, adaptive RK45, and implicit Radau. Their convergence properties are characterised on both the RSF system and a smooth reference problem.

Official source

https://infoscience.epfl.ch/entities/publication/42e3dd90-f19f-49e7-9a45-87943199d0dd

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2026

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/42e3dd90-f19f-49e7-9a45-87943199d0dd

About this result

Related concepts (32)

Numerical methods for ordinary differential equations

Numerical methods for ordinary differential equations are methods used to find numerical approximations to the solutions of ordinary differential equations (ODEs). Their use is also known as "numerical integration", although this term can also refer to the computation of integrals. Many differential equations cannot be solved exactly. For practical purposes, however – such as in engineering – a numeric approximation to the solution is often sufficient. The algorithms studied here can be used to compute such an approximation.

Verlet integration

Verlet integration (vɛʁˈlɛ) is a numerical method used to integrate Newton's equations of motion. It is frequently used to calculate trajectories of particles in molecular dynamics simulations and computer graphics. The algorithm was first used in 1791 by Jean Baptiste Delambre and has been rediscovered many times since then, most recently by Loup Verlet in the 1960s for use in molecular dynamics. It was also used by P. H. Cowell and A. C. C.

Numerical integration

In analysis, numerical integration comprises a broad family of algorithms for calculating the numerical value of a definite integral, and by extension, the term is also sometimes used to describe the numerical solution of differential equations. This article focuses on calculation of definite integrals. The term numerical quadrature (often abbreviated to quadrature) is more or less a synonym for numerical integration, especially as applied to one-dimensional integrals.

Related publications (32)

Emergence of complexity in a frictional system: reproducing earthquake statistics

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