Results 41 to 50 of about 2,383 (165)

Modified Iterative Runge-Kutta-Type Methods for Nonlinear Ill-Posed Problems [PDF]

Numerical Functional Analysis and Optimization, 2016
This work is devoted to the convergence analysis of a modified Runge-Kutta-type iterative regularization method for solving nonlinear ill-posed problems under a priori and a posteriori stopping rules. The convergence rate results of the proposed method can be obtained under a Holder-type sourcewise condition if the Frechet derivative is properly scaled
Pornsawad, Pornsarp, Böckmann, Christine   +1 more
openaire   +3 more sources

A quasi-boundary value method for regularizing nonlinear ill-posed problems

Electronic Journal of Differential Equations, 2009
In this article, a modified quasi-boudary regularization method for solving nonlinear backward heat equation is given. Sharp error estimates for the approximate solutions, and numerical examples to illustrate the effectiveness our method are provided.
Dang Duc Trong, Pham Hoang Quan, Nguyen Huy Tuan   +2 more
doaj  

Inversion of geothermal heat flux in a thermomechanically coupled nonlinear Stokes ice sheet model [PDF]

The Cryosphere, 2016
We address the inverse problem of inferring the basal geothermal heat flux from surface velocity observations using a steady-state thermomechanically coupled nonlinear Stokes ice flow model.
H. Zhu, N. Petra, G. Stadler, T. Isaac, T. J. R. Hughes, O. Ghattas   +5 more
doaj   +1 more source

Machine Learning Enhanced Artificial Bee Colony for Solving Inverse Problems: Surrogate-Guided Reconstruction under Measurement Noise

EDRAAK
Inverse problems are fundamental to a variety of scientific and engineering problems, but are commonly ill-posed, nonlinear, and sensitive to measurement errors.
Habeeb Al-thabhawee, Ghassan AL-Thabhawee, Hussein Alkattan   +2 more
doaj   +1 more source

Stabilized quasi-reversibility method for a class of nonlinear ill-posed problems

Electronic Journal of Differential Equations, 2008
In this paper, we study a final value problem for the nonlinear parabolic equation $$displaylines{ u_t+Au =h(u(t),t),quad ...
Nguyen Huy Tuan, Dang Duc Trong
doaj  

Statistical inverse inference for solving the first kind of nonlinear Fredholm integral equation

Applied Mathematics in Science and Engineering
Inverse problems, widely applied in geology, oceanography, and geophysics, are often ill-posed, presenting significant challenges. This study addresses the first kind of nonlinear Fredholm integral equation derived from gravity measurement and magnetic ...
Ailing Wang, Guoqing Chen, Andrei Volodin, Piyapatr Busababodhin   +3 more
doaj   +1 more source

Inverse Problems in Pump–Probe Spectroscopy

Photochem
Ultrafast pump–probe spectroscopic studies allow for deep insights into the mechanisms and timescales of photophysical and photochemical processes. Extracting valuable information from these studies, such as reactive intermediates’ lifetimes and coherent
Denis S. Tikhonov, Diksha Garg, Melanie Schnell   +2 more
doaj   +1 more source

Stochastic asymptotical regularization for nonlinear ill-posed problems

Inverse Problems
Abstract Recently, the stochastic asymptotical regularization (SAR) has been developed in Zhang and Chen (2023 Inverse Problems 39 015007) for the uncertainty quantification of the stable approximate solution of linear ill-posed inverse problems.
Haie Long, Ye Zhang
openaire   +2 more sources

Continuous dependence on modeling for nonlinear ill-posed problems

Journal of Mathematical Analysis and Applications, 2009
The authors study the nonlinear ill-posed Cauchy problem \[ \frac{du}{dt}=Au(t)+h(t,u(t)),\;\;u(0)=\varkappa, \] where \(A\) is a positive self-adjoint operator on a Hilbert space \(\mathcal{H}\) and \(h:[0,T)\times\mathcal{H}\to\mathcal{H}\) is a uniformly Lipschitz function with respect to both variables.
Campbell Hetrick, Beth M., Hughes, Rhonda J.   +1 more
openaire   +2 more sources

Data assimilation in 2D hyperbolic/parabolic systems using a stabilized explicit finite difference scheme run backward in time

Applied Mathematics in Science and Engineering
An artificial example of a coupled system of three nonlinear partial differential equations generalizing 2D thermoelastic vibrations, is used to demonstrate the effectiveness, as well as the limitations, of a non iterative direct procedure in data ...
Alfred S. Carasso
doaj   +1 more source