Stability of Finite Difference Schemes on Non-uniform Spatial-Time-Grids
نویسندگان
چکیده
A bstract. The three level operator finite difference schemes on nonuniform on time grids in llilbert spaces of finite dimension are consid ered. A priori estimates for uniform stability on the initial conditions are received under natural assumptions on operators and non uniform time grids. The results obtained here are applied to study stability o f the three levels weighted schemes of second order approximation О (/i2 + r „ ) for some hyperbolic and parabolic equations of the second order. It is es sential to note that the schemes of raised order of approximation are constructed here on standard stencils which are used in finite difference approximation techniques.
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