Stable explicit stepwise marching scheme in ill-posed time-reversed viscous wave equations

DOI10.1080/17415977.2015.1124429zbMath1348.65156OpenAlexW2311440918MaRDI QIDQ2831866

Alfred S. Carasso

Publication date: 3 November 2016

Published in: Inverse Problems in Science and Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/17415977.2015.1124429

zbMATH Keywords

viscous wave equationimage deblurringquasi-reversibility methodirreversible systemsnon-integer power LaplacianFFT Laplacian stabilizationforward or backward time marchingstabilized explicit scheme

Mathematics Subject Classification ID

Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Numerical methods for ill-posed problems for boundary value problems involving PDEs (65N20)

Related Items (5)

Stabilized Richardson leapfrog scheme in explicit stepwise computation of forward or backward nonlinear parabolic equations ⋮ Stabilized backward in time explicit marching schemes in the numerical computation of ill-posed time-reversed hyperbolic/parabolic systems ⋮ Stable explicit stepwise marching scheme in ill-posed time-reversed 2D Burgers' equation ⋮ Computing ill-posed time-reversed 2D Navier–Stokes equations, using a stabilized explicit finite difference scheme marching backward in time ⋮ Stabilized leapfrog scheme run backward in time, and the explicit O(Δ t)² stepwise computation of ill-posed time-reversed 2D Navier–Stokes equations

Cites Work

• Computing eigenmodes of elliptic operators using radial basis functions
• On the computation of a very large number of eigenvalues for selfadjoint elliptic operators by means of multigrid methods
• Compensating operators and stable backward in time marching in nonlinear parabolic equations
• Reconstructing the past from imprecise knowledge of the present: Effective non‐uniqueness in solving parabolic equations backward in time
• Least Squares Methods for Ill-Posed Problems with a Prescribed Bound

This page was built for publication: Stable explicit stepwise marching scheme in ill-posed time-reversed viscous wave equations