×

On convergence of centered difference schemes for dynamic problems of the theory of elasticity. (Russian) Zbl 0575.73026

The paper is concerned to the problem of estimating the degree of accuracy of the finite difference scheme approximating the systems of equations of dynamic elasticity. The equations being in question are of the hyperbolic type of the first order. By introducing integral operators defining the mean values of the functions involved, the finite difference schemes are constructed due to time as well as space coordinates. The author analyses the problem of stability as well as of the degree of accuracy and the velocity of convergence of the proposed finite difference schemes (called by the author the centered difference scheme). A series of relevant lemmas are formulated and proved. The operator formulation has been applied.
Reviewer: V.Brčić

MSC:

74B99 Elastic materials
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
39A70 Difference operators
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs