Holistic discretisation of dynamical PDEs: some theory
نویسنده
چکیده
where: x is position in one or more spatial dimensions; u(x, t) is some scalar or vector field, such as fluid velocity and pressure; L is a dissipative linear operator, such as ∇; f(u) includes other autonomous terms representing nonlinear advection, reaction, etc.; and q(u, t) is some time dependent control or possibly stochastic forcing [22]. Among many physically relevant examples are Burgers’ equation [1, e.g.], the Brusselator [9, §3], Liouville’s equation [13] and the Swift–Hohenberg equation [4, e.g.].
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