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Ill-Posed Point Neuron Models [PDF]
The Journal of Mathematical Neuroscience, 2016 We show that point-neuron models with a Heaviside firing rate function can be ill posed. More specifically, the initial-condition-to-solution map might become discontinuous in finite time. Consequently, if finite precision arithmetic is used, then it is virtually impossible to guarantee the accurate numerical solution of such models. If a smooth firing
Nielsen, Bjørn Fredrik +1 more
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On the discrete linear ill‐posed problems
Mathematical Modelling and Analysis, 1999 An inverse problem of photo‐acoustic spectroscopy of semiconductors is investigated. The main problem is formulated as the integral equation of the first kind.
A. A. Stepanov
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Ill-posed equations with transformed argument [PDF]
Abstract and Applied Analysis, 2003 We discuss the operator transforming the argument of a function in the L2-setting. Here this operator is unbounded and closed. For the approximate solution of ill-posed equations with closed operators, we present a new view on the Tikhonov regularization.
Simone Gramsch, Eberhard Schock
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Regularization of exponentially ill-posed problems
Numerical Functional Analysis and Optimization, 2000 Linear and nonlinear inverse problems which are exponentially ill-posed arise in heat conduction, satellite gradiometry, potential theory and scattering theory. For these problems logarithmic source conditions have natural interpretations whereas standard Holder-type source conditions are far too restrictive.
Thorsten Hohage
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Economic Cycles of Carnot Type
Entropy, 2021 Originally, the Carnot cycle was a theoretical thermodynamic cycle that provided an upper limit on the efficiency that any classical thermodynamic engine can achieve during the conversion of heat into work, or conversely, the efficiency of a ...
Constantin Udriste +2 more
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Discrete and Continuous Models and Applied Computational Science, 2023 The paper describes a grid method for solving an ill-posed problem for the Fredholm equation of the first kind using the A. N. Tikhonov regularizer. The convergence theorem for this method was formulated and proved.
Aleksandr A. Belov
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On a time fractional diffusion with nonlocal in time conditions
Advances in Difference Equations, 2021 In this work, we consider a fractional diffusion equation with nonlocal integral condition. We give a form of the mild solution under the expression of Fourier series which contains some Mittag-Leffler functions. We present two new results.
Nguyen Hoang Tuan +3 more
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RUDN Journal of Informatization in Education, 2020 Problem and goal. Computer technologies are now widely used in applied research aimed at obtaining new scientific knowledge. These studies used the method of computer modeling and computing experiment, from which it is possible to study the properties of
Viktor S. Kornilov
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Ill-posed problems in thermomechanics
Applied Mathematics Letters, 2009 Several thermomechanical models have been proposed from a heuristic point of view. A mathematical analysis should help to clarify the applicability of these models, among those recent thermal or viscoelastic models. Single-phase-lag and dual-phase-lag heat conduction models can be interpreted as formal expansions of delay equations. The delay equations
Michael Dreher +2 more
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On Tikhonov's Method for Ill-Posed Problems [PDF]
Mathematics of Computation, 1974 For Tikhonov’s regularization of ill-posed linear integral equations, numerical accuracy is estimated by a modulus of convergence, for which upper and lower bounds are obtained. Applications are made to the backward heat equation, to harmonic continuation, and to numerical differentiation.
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