Matematik modellashtirish yordamida murakkab jarayonlardagi tarqalish tenglamalarining taqribiy yechimlarini topish usullari
Methods for finding approximate solutions of diffusion-type equations in complex processes using mathematical modeling
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The paper studies methods for finding approximate solutions of parabolic spreading (diffusion-type) equations that describe complex processes such as heat conduction, diffusion, filtration and population spread. Explicit, implicit and weighted (Crank–Nicolson) finite difference schemes are constructed for linear and nonlinear equations, and their stability conditions and orders of convergence are analysed. The Thomas (sweep) algorithm and Picard iteration are used for solving the resulting systems. Numerical experiments on a test problem with a known exact solution compare the accuracy and stability of the schemes, and practical recommendations are given.
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