A novel class of linearly implicit energy-preserving schemes for conservative systems

TL;DR

This paper introduces a new class of linearly implicit, energy-preserving numerical schemes for conservative differential equations, combining scalar auxiliary variable and splitting methods to improve efficiency while maintaining energy conservation.

Contribution

The paper develops a novel class of linearly implicit energy-preserving schemes using scalar auxiliary variables and splitting, with rigorous stability and error analysis.

Findings

Unconditionally energy stable schemes

Linearly implicit systems with reduced computational cost

Numerical experiments confirm theoretical properties

Abstract

We consider a kind of differential equations d/dt y(t) = R(y(t))y(t) + f(y(t)) with energy conservation. Such conservative models appear for instance in quantum physics, engineering and molecular dynamics. A new class of energy-preserving schemes is constructed by the ideas of scalar auxiliary variable (SAV) and splitting, from which the nonlinearly implicit schemes have been improved to be linearly implicit. The energy conservation and error estimates are rigorously derived. Based on these results, it is shown that the new proposed schemes have unconditionally energy stability and can be implemented with a cost of solving a linearly implicit system. Numerical experiments are done to confirm these good features of the new schemes.