Stable explicit time marching in well-posed or ill-posed nonlinear parabolic equations

DOI10.1080/17415977.2015.1110150zbMath1348.65128OpenAlexW2343072877MaRDI QIDQ2831860

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/10.1080/17415977.2015.1110150

zbMATH Keywords

quasi-reversibility methodnonlinear image deblurringFFT Laplacian stabilizationforward or backward nonlinear parabolic equationsnoninteger power Laplacianstabilized explicit schemeVan Cittert iteration

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Numerical methods for ill-posed problems for initial value and initial-boundary value problems involving PDEs (65M30)

Related Items (8)

Stable backward diffusion models that minimise convex energies ⋮ Stabilized Richardson leapfrog scheme in explicit stepwise computation of forward or backward nonlinear parabolic equations ⋮ Final value problem for nonlinear time fractional reaction-diffusion equation with discrete data ⋮ A discrete theory and efficient algorithms for forward-and-backward diffusion filtering ⋮ 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

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• 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
• Eigenvalues of the Laplacian in Two Dimensions
• Reconstructing the past from imprecise knowledge of the present: Effective non‐uniqueness in solving parabolic equations backward in time
• Bounds for the fundamental solution of a parabolic equation
• Least Squares Methods for Ill-Posed Problems with a Prescribed Bound

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