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Article · Differential Equations · December 1, 2021
On Optimal Discretization of Solutions of the Heat Equation and the Limit Error of the Optimum Computing Unit
A. B. Utesov, A. A. Bazarkhanova
Abstract
In the framework of the general statement of the operator reconstruction problem, the problem of discretization of solutions of the heat equation with the initial condition $$f $$ in the periodic anisotropic Sobolev class is solved by computing units constructed from the trigonometric Fourier coefficients $$\hat {f}(m) $$ in the metric of the space $$L^{ \infty ,q} $$ , $$q\geq 2$$ . The error $$\bar {\varepsilon }_{N}$$ of computing the trigonometric Fourier coefficients of the initial condition $$f $$ corresponding to the optimal computing unit is also found, and the sharpness of the order of the error $$\bar {\varepsilon }_{N} $$ is proved.
Differential Equations and Boundary ProblemsMathematical Approximation and IntegrationNumerical methods in inverse problemsheat equationerror estimation
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