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This article offers a comprehensive overview of the results obtained through numerical methods in solving the minimal surface equation, along with exploring the applications of minimal surfaces in science, technology, and architecture. The content is enriched with practical examples highlighting the diverse applications of minimal surfaces.

Based on an example, we describe how outcomes of computational experiment can be employed for study of stability of numerical algorithm, provided that related theoretical propositions are not proven yet. More precisely, we propose a systematic and generalized methodology, how to investigate the influence of the weight functions α(x) and β(x), present in the integral boundary conditions, on the stability of difference schemes, for some class of parabolic equations. The ground of the methodology is the investigation of the spectrum of a matrix, defining the transition to the upper layer of the difference scheme. Spectral structure of this matrix is analysed by both analytic method and computational experiment.

The method for calculating the specific conductivity tensor of an anisotropically conductive medium, proposed in this paper, distinguishes itself by the simplicity of physical measurements: it suffices to make an equally thick rectangle-shaped sample with four electrodes fixed on its sides and to take various measurements of current intensity and differences of potentials. The necessary mathematical calculations can be promptly performed, even without using a complex computing technique. The accuracy of the results obtained depends on the dimensions of the sample and on the ratios of the conductivity tensor components.

A model of the moisture diffusion in wood under isothermal conditions taking into consideration coating of the surface of a specimen is presented in a 2-D-in-space formulation. A reliability of a corresponding 1-D model is investigated for a simulation of moisture movement in 2-D medium. This paper presents a technique to determine the width as well as the degree of edges coating of the specimen making the 1-D model relevant for 2-D medium. This technique bases on the computer simulation of 2-D moisture diffusion to estimate the reliability of the corresponding 1-D model. In the technique, approximate coefficients of the diffusion and surface emission may be employed if accurate values of these coefficients are unknown.

The distribution of neutron population in nuclear reactor is described by using transport equations. One of possible approximations of neutron transport equation is given by the neutron diffusion equation. The paper presents numerical solution method of one group neutron diffusion equation with one group of delayed neutrons.