Browsing by Author "Kanca, Fatma"

Now showing 1 - 8 of 8

Citation Count: 3
Analysis for Two-Dimensional Inverse Quasilinear Parabolic Problem by Fourier Method
(Taylor & Francis Ltd, 2021) Kanca, Fatma; Baglan, Irem; Bilgisayar Mühendisliği Bölümü
In this work, two-dimensional inverse quasi-linear parabolic problem with periodic boundary and integral overdetermination conditions is investigated. The formal solution is obtained by the Fourier approximation. Under some natural regularity and consistency conditions on the input data,the existence, uniqueness and continuously dependence upon the data of the solution are proved by iteration method. The inverse problem is first examined by linearization and then used implicit finite difference scheme for the numerical solution. Also predictor corrector method is considered in the numerical approach. Some results on the numerical solution with two examples are presented with figures and tables. The sensitivity of the scheme with respect to noisy overdetermination data is illustrated.
Citation Count: 0
Fourier Method for an Existence of Quasilinear Inverse Pseudo-Parabolic Equation
(Tarbiat Modares Univ, Acecr, 2024) Kanca, Fatma; Kanca, Fatma; Mishra, Vishnu Narayan; Bilgisayar Mühendisliği Bölümü
In this work, the inverse quasi -linear pseudo -parabolic problem was investigated. We demonstrated the solution by the Fourier approximation. The inverse problem was first examined by linearizing and then used implicit finite difference schema for the numerical solution.
Citation Count: 0
Fourier Method for Higher Dimensional Inverse Quasi-Linear Parabolic Problem
(Wiley, 2021) Kanca, Fatma; Kanca, Fatma; Bilgisayar Mühendisliği Bölümü
In this work, higher-dimensional inverse quasi-linear parabolic problem was investigated. We demonstrated the solution by the Fourier approximation. The inverse problem was first examined by linearizing and then used implicit finite difference schema for the numerical solution.
Citation Count: 2
Identification Problem of a Leading Coefficient To the Time Derivative of Parabolic Equation With Nonlocal Boundary Conditions
(Springer international Publishing Ag, 2019) Kanca, Fatma; Mishra, Vishnu Narayan; Bilgisayar Mühendisliği Bölümü
In this study, the problem of determining the time-dependent leading coefficient to the time derivative of heat equation with nonlocal boundary and integral addition conditions is considered. The existence and uniqueness of a solution of the inverse problem under considerations are established. Some results on the numerical solution with an example are presented.
Citation Count: 5
Inverse Problem for a Time Fractional Parabolic Equation With Nonlocal Boundary Conditions
(Mdpi, 2022) Kanca, Fatma; Kanca, Fatma; Ozbilge, Emre; Bilgisayar Mühendisliği Bölümü
This article considers an inverse problem of time fractional parabolic partial differential equations with the nonlocal boundary condition. Dirichlet-measured output data are used to distinguish the unknown coefficient. A finite difference scheme is constructed and a numerical approximation is made. Examples and numerical experiments, such as man-made noise, are provided to show the stability and efficiency of this numerical method.
Citation Count: 2
Inverse Problem for Euler-Bernoulli Equation With Periodic Boundary Condition
(Univ Nis, Fac Sci Math, 2018) Kanca, Fatma; Baglan, Irem; Bilgisayar Mühendisliği Bölümü
In this work the inverse coefficient problem for Euler-Bernoulli equation with periodic boundary and integral addition conditions is investigated. Under some natural regularity and consistency conditions on the input data the existence, uniqueness and continuously dependence upon the data of the solution are shown by using the generalized Fourier method. Numerical tests using the implicit finite difference scheme combined with an iterative method are presented and discussed. Also an example is presented with figures.
Citation Count: 0
Solution of Inverse Euler-Bernoulli Problem With Integral Overdetermination and Periodic Boundary Conditions
(Tarbiat Modares Univ, Acecr, 2022) Kanca, Fatma; Kanca, Fatma; Mishra, Vishnu Narayan; Bilgisayar Mühendisliği Bölümü
In this work, we tried to find the inverse coefficient in the Euler problem with over determination conditions. It showed the existence, stability of the solution by iteration method and linearization method was used for this problem in numerical part. Also two examples are presented with figures.
Citation Count: 2
Solution of the Boundary-Value Problem of Heat Conduction With Periodic Boundary Conditions
(Springer, 2020) Kanca, Fatma; Baglan, I.; Bilgisayar Mühendisliği Bölümü
We investigate the solution of the inverse problem for a linear two-dimensional parabolic equation with periodic boundary and integral overdetermination conditions. Under certain natural regularity and consistency conditions imposed on the input data, we establish the existence, uniqueness of the solution, and its continuous dependence on the data by using the generalized Fourier method. In addition, an iterative algorithm is constructed for the numerical solution of the problem.