A stabilized backward-marched explicit finite difference scheme can recover plausible initial data from final-time images in a nonlinear coupled sound and heat flow model, but only for short time horizons.
Data assimilation in 2D nonlinear advection diffusion equations, using an explicit 10 stabilized leapfrog scheme run backwrd in time
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Data assimilation in 2D nonlinear coupled sound and heat flow, using a stabilized explicit finite difference scheme marched backward in time
A stabilized backward-marched explicit finite difference scheme can recover plausible initial data from final-time images in a nonlinear coupled sound and heat flow model, but only for short time horizons.