  Linear differential equations are ubiquitous in science and engineering.
Quantum computers can simulate quantum systems, which are described by a
restricted type of linear differential equations. Here we extend quantum
simulation algorithms to general inhomogeneous sparse linear differential
equations, which describe many classical physical systems. We examine the use
of high-order methods to improve the efficiency. These provide scaling close to
$\Delta t^2$ in the evolution time $\Delta t$. As with other algorithms of this
type, the solution is encoded in amplitudes of the quantum state, and it is
possible to extract global features of the solution.

Quantum Physics;Numerical Analysis;Numerical Analysis