Source inversion of heat conduction from a finite number of observation data

Mathematical modelling and method for solving a parametric identification problem for self-test of measuring devices

“…The values T u , T v are obtained via substitution of uᾱ 1 , vᾱ 2 in system (2). For obtaining values R(u) and R(v), we use equation (1). The quantities of (R(u)), (R(v)) and are calculated according to (24) and (25).…”

“…The regularized algorithms are initially widely used to solve different inverse problems in engineering. Thus, in papers [1][2][3][4], the authors applied regularization methods for solving inverse problems of thermal conductivity. Cordier et al [5], consider a model to a 2D cylinder wake flow where Tikhonov regularization methods of different orders are used to obtain the most efficient solutions.…”

Introduction to Numerical Approaches for Forward and Inverse Heat Transfer Problems

“…We can compare the residual at time T and attempt some corrections to U 0 based on this residual such that the propagated solution at t ¼ T best matches observations. In the case of only a finite subset of observations, interpolation techniques can be utilized to complete the profile at t ¼ T across all values of x [7] prior to regularization to obtain an approximate smooth and continuous uT ðÞ heat profile.…”

General Inhomogeneous Discrete Linear Partial Differential Equations with Constant Coefficients on the Whole Spaces

“…Furthermore, we shall establish error estimates for our solutions because practical data contain error and noises. In the second part, we will construct the approximate solutions for discrete differential equations, following a recent general idea (see [2]). Furthermore, we will reveal their inversions.…”