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Application of interpolation theory to the analysis of the convergence rate for finite difference schemes of parabolic type. (English) Zbl 0948.46018

In the case of the initial-boundary problem for the heat equation, the authors show how the theory of interpolation of function spaces is used for the rate estimate of convergence of finite difference schemes.

MSC:

46B70 Interpolation between normed linear spaces
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
47F05 General theory of partial differential operators
35K20 Initial-boundary value problems for second-order parabolic equations
35K15 Initial value problems for second-order parabolic equations
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