...Magda Joachimiak Purpose In this paper, the Cauchy-type problem for the Laplace equation was solved in the rectangular domain with the use of the Chebyshev polynomials. The purpose of this paper is to present an optimal choice of the regularization parameter for the inverse problem, which allows...

... and, additionally, on one of the boundaries, the heat flux distribution was selected. The purpose of consideration was to determine the distribution of temperature on a section of the boundary of the investigated domain (boundary Γ₁) and find proper method for the problem regularization. Design...

... coefficient identification problem is inverse and ill-posed, and therefore, to obtain a stable solution, a non-linear regularized least-squares approach is used. For the numerical discretization of the orthotropic heat equation, the finite-difference method is applied, while the non-linear minimization...

... combined with a regularized nonlinear minimization is performed using the MATLAB toolbox routine lsqnonlin. Findings Numerical results presented for three examples show the efficiency of the computational method and the accuracy and stability of the numerical solution even in the presence...

... Lesnic can be contacted at: amt5ld@maths.leeds.ac.uk © Emerald Group Publishing Limited 2013 Inverse problem Method of fundamental solutions Non‐linear optimization Regularization Thermography Shape identification Optimization techniques Heat transfer ϵ=random noise...