On stability estimates in the Marcinkiewicz theorem and its generalization

1992 ◽  
pp. 243-250
Author(s):  
L. Golinskii ◽  
G. Chistyakov
Keyword(s):  
Stability Estimates ◽  
Marcinkiewicz Theorem

scholarly journals An Inverse Source Problem for the Generalized Subdiffusion Equation with Nonclassical Boundary Conditions

2021 ◽  
Vol 5 (3) ◽  
pp. 63
Author(s):  
Emilia Bazhlekova
Keyword(s):  
Boundary Conditions ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Stability Estimates ◽  
Inverse Source Problem ◽  
Time Data ◽  
Final Time ◽  
Generalized Eigenfunction ◽  
The One ◽  
Initial Boundary Value

An initial-boundary-value problem is considered for the one-dimensional diffusion equation with a general convolutional derivative in time and nonclassical boundary conditions. We are concerned with the inverse source problem of recovery of a space-dependent source term from given final time data. Generalized eigenfunction expansions are used with respect to a biorthogonal pair of bases. Existence, uniqueness and stability estimates in Sobolev spaces are established.

Numerical ranges and stability estimates

1993 ◽  
Vol 13 (1-3) ◽  
pp. 241-249 ◽  
Author(s):  
M.N. Spijker
Keyword(s):  
Stability Estimates

Numerical solution of a source identification problem: Almost coercivity

2019 ◽  
Vol 27 (4) ◽  
pp. 457-468 ◽  
Author(s):  
Allaberen Ashyralyev ◽  
Abdullah Said Erdogan ◽  
Ali Ugur Sazaklioglu
Keyword(s):  
Numerical Solution ◽  
Source Identification ◽  
Identification Problem ◽  
Second Order ◽  
Numerical Results ◽  
Difference Schemes ◽  
Stability Estimates ◽  
Order Of Accuracy ◽  
Accuracy Difference ◽  
Coercive Stability

Abstract The present paper is devoted to the investigation of a source identification problem that describes the flow in capillaries in the case when an unknown pressure acts on the system. First and second order of accuracy difference schemes are presented for the numerical solution of this problem. Almost coercive stability estimates for these difference schemes are established. Additionally, some numerical results are provided by testing the proposed methods on an example.

scholarly journals On the numerical solutions for nonlinear Volterra-Fredholm integral equations

2022 ◽  
Vol 40 ◽  
pp. 1-11
Author(s):  
Parviz Darania ◽  
Saeed Pishbin
Keyword(s):  
Nonlinear System ◽  
Integral Equations ◽  
Numerical Experiments ◽  
Numerical Solutions ◽  
Coefficient Matrix ◽  
Collocation Methods ◽  
Fredholm Integral Equations ◽  
Stability Estimates ◽  
Lower Triangular ◽  
Theoretical Results

In this note, we study a class of multistep collocation methods for the numerical integration of nonlinear Volterra-Fredholm Integral Equations (V-FIEs). The derived method is characterized by a lower triangular or diagonal coefficient matrix of the nonlinear system for the computation of the stages which, as it is known, can beexploited to get an efficient implementation. Convergence analysis and linear stability estimates are investigated. Finally numerical experiments are given, which confirm our theoretical results.

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