Реалізація неявних різницевих схем розв’язання задач математичної фізики засобами табличного процесора MS Excel
Journal Title: Математичне моделювання - Year 2017, Vol 1, Issue 1
Abstract
IMPLEMENTATION OF IMPLICIT DIFFERENCE SCHEMES TO SOLVE THE MATHEMATICAL PHYSICS PROBLEMS USING MS EXCEL SPREADSHEET Karimov I.K., Karimov G.I. Abstract The implementation of difference schemes is connected to the high volume of computations and is usually carried out on a PC using on a program written in one of the programming languages. For professionals whose main job is not related to programming, such an approach leads to some difficulties, which defines the necessity of finding alternative ways to implement difference schemes. The purpose of the study is to research the specifics of using the MS Excel spreadsheet for the implementation of implicit difference schemes; the task is to develop and test the applicable algorithm using the example of solving the boundary value problem for a typical parabolic equation - the heat equation. To solve the problem, an implicit difference scheme is used, which leads to the necessity of solving the system of linear algebraic equations of the three diagonal forms using the marching algorithm at each time step. A new approach to the implementation of the described algorithm, based on the use of MS Excel spreadsheet, is proposed. An algorithm and results of the solution of the boundary value of heat conduction based of the proposed approach are given. The data obtained in this way allows us to analyze the simulated process in all aspects of interest to the researcher: to answer a number of questions regarding the nature of the temperature distribution in the investigated area, to determine the time of attaining one or another temperature at a given point, temperature differences, etc. The most attractive features of the proposed approach should include the absence of direct programming, the simplicity of computer implementation, the ease and natural presentation of the results. Especially note the appeal of the application of the proposed approach in the learning process. Avoiding the programming allows students to reduce the component of modeling, not directly related to future professional activities, and to concentrate efforts on forming skills of mathematical modeling and analysis of the specifics of the investigated process. As a result, the learning process becomes more creative, theory is better absorbed, motivation and interest in application of methods of mathematical modeling is increased. The specifics of the application of the proposed approach in some cases (nonlinear problems, two-dimensional problems, etc.) require further research. References [1] Samarsky A. A. Teoriya raznostnyh shem. [Theory of difference schemes] – Moscow: Nauka, 1983. – 616 p. [2] Godunov S.K., Ryabenky V.S. Raznostnye shemy. Vvedenie v teoriyu. [Difference schemes. Introduction to the theory] – Moscow: Nauka, 1973. – 400 p. [3] Feldman L.P., Petrenko A.I., Dmitrieva O.A. Chiselni metody v informatici. [Numerical methods in computer science] – K .: Publishing group VNV, 2006. – 480 p. [4] Paskonov V.M., Polezhaev V.I., Chudov L.A. Chislennoe modelirovanie processov teplo- i massoperenosa. [Numerical simulation of heat and mass transfer processes] – Moscow: Nauka, 1984. – 288 p. [5] Ogurtsov A.P., Samokhvalov S.E. Chislennye metody issledovaniya gidrodinamicheskih and teplomassoperemosnyh processov staleplavilnogo poizvodstva. [Numerical methods of the investigation of hydrodynamic and heat and mass transfer processes on steel production]– K .: Naukova Dumka, 1993. – 220 p. [6] Ogurtsov A.P., Mamaev L.N., Karimov I.K. Matematicheskie metody i modeli v rasschetax ne EVM. [Mathematical methods and models in calculations on computers] – K .: ISMO, 1997. – 192 p. [7] Kundrat A.M., Kundrat M.M. Naukovo-tehnichni obchislennya zasobami MathCAD i MS Excel. [Scientific and technical computing by means of MathCAD and MS Excel] – Rivne: NUVGP, 2014 – 252 p. [8] Porshnev S.V., Belenkova I.V. Chislennye metody na baze MathCAD [Numerical methods based on MathCAD], – SPb .: BHV-Petersburg, 2005. – 464 p. [9] Karimov I.K., Karimov G.I., Nuzhna S.A. Realizaciya riznecevyh shem zasobami tablichnogo processora MS Excel/Problemy matematichnogo modelyuvannya[Implementation of difference schemes using means of MS Excel spreadsheet/ Problems of mathematical modeling]: Materials Allukr. sci. method. conf., 24–26 May. 2017 – Dnepr: Bila K.O., 2017. – P.130–132.
Authors and Affiliations
І. К. Карімов, Г. І. Карімов
Keywords
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