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Тезисы докладов

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A new efficient direct method for numerical solving of mathematical physics problems: heat conduction, elasticity problems and plate theory are suggest and base. The method are grounds on conjugate-operator structure of discrete analogue of initial problems: begin{equation}R^*_h,{bf w^h},=,{bf f^h}, end{equation} begin{equation} {bf w^h},=,K_h{bf q^h}, end{equation} begin{equation}{bf q^h},=,R_h,{bf u^h}, end{equation} $${bf u^h} in H^*_h, quad {bf w^h} in H_h. $$ The main idea is consist in successive, step-by-step, determination ,,${bf w^h}$,, from (1), then ,,${bf q^h}$,,from equation (2) and ,,${bf u^h}$,, from (3). The method allows to calculate the difference solution for the domains of a standard shape: begin{itemize} item[$bullet$] for one-dimensional heat conduction problem for ,,$8,N$,, arithmetic operations; item[$bullet$] for Laplace equation for the number arithmetic operations which in proportion ,,$N,ln(N);$,, item[$bullet$] for two-dimensional elasticity problems with constant coefficients for the number arithmetic operations which in proportion ,,$N,N^{frac{1}{2}};$,, item[$bullet$] for one-dimensional plate theory problem for ,,$19,N$,, arithmetic operations; item[$bullet$] for two-dimensional plate theory problem with constant rigidity for the number arithmetic operations which in proportion ,,$N,N^{frac{1}{2}},$,, end{itemize} where ,,$N$,, is the number of unknowns.

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