A POLINOMIAL APPROXIMATION METHOD FOR THE STEP OPERATOR OF THE HEAT CONDUCTIVITY EQUATION
O. M. Kozyrev, V. P. Litvinov
VANT. Ser.: Mat. Mod. Fiz. Proc 2012. Вып.4. С. 3-12.
Given here is for solving the boundary-value problems of the heat conductivity equation. The method is based on constructing a difference step operator in the form of an operator polynomial. The operator polynomial is constructed in the space of Fourier images using Chebyshev and Lanczos polynomials. The solution algorithm represents explicit stepwise calculations and is implemented in the form of {it predictor-corrector} scheme. The method is easy to implement and can be efficiently parallelized. The method is described by the example of Cauchy problem for the linear heat conductivity equation. Results of numerical solutions for some well-known test problems are presented.Keywords: heat conductivity equation, Fourier image, Chebyshev and Lanczos polynomial.
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