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\propto h^{\alpha+1 }).</math> The HOLL discretization (4.4) [[Rate of convergence|converges]] with order <math>\alpha</math> to the solution of nonlinear ODEs, but it match the solution of the linear ODEs.
HOLL discretizations can be derived in two ways:<ref name= ":8"/><ref name= ":3"/><ref name= ":2"/><ref name=":1" /> 1) (quadrature-based) by approximating the integral representation (4.2) of '''r'''; and 2) (integrator-based) by using a numerical integrator for the differential representation of '''r''' defined by
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