Proceeding from given experimental data, i.e., observation times and measurements, the minimum least squares distances of measured data from a fitting criterion are computed, which depends on the solution of the dynamic system. Various types of one-dimensional partial differential equations are permitted, also hyperbolic ones describing shock waves. Advection, diffusion, transport, or related equations can be solved successfully by non-oscillatory discretization schemes, even with non-continuous initial or boundary conditions.
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