Browsing by Author "Temirkul A.Sh"

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    The solution of the heat equation in domains with moving boundaries by the Integral Error Functions method
    (faculty of engineering and natural sciences, 2013) Temirkul A.Sh
    In mathematics , development of new analytical methods of solution of the heat transfer problems is very important for various applications because it enables one to analyze an interrelationship of various input parameters on the dynamics of investigating phenomena, while the use of numerical methods is a problem when the number of parameters is great. And from mathematical point of view, most mathematical models based on Verigin, Stefan and inverse Stefan type boundary value problems. Such problems are among the most complicated, formidable and difficult problems in the theory of nonlinear parabolic equations in mathematical physics, since the corresponding integral equations are singular and require new approaches in solving problems analytically and numerically and also which long with the desired solutions of the equations, moving boundaries have to be found. In some cases, heat potentials can be constructed by which the boundaryvalue problems can be reduced to integral equations. However, in the case of domains that are degenerate at the initial time, additional difficulties arise due to the singularity of the integral* equations, which belong to the class of pseudoVolterra equations that are unsolvable inthe general case bythe method of successive approximations. These results are obtained by S.N. Kharin [2]. The method of solving heat transfer problems with moving boundaries and phase transformation is represented'by Integral Error Functions and its properties. The results indicate that Integral Error Functions enable to solve, many practical problems described above in the easier way than classical methods, and could be implemented into the course of teaching mathematical physics, as special methods of solving heat transfer problems with moving boundaries.