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New analysis of the Du Fort-Frankel methods. (English) Zbl 1254.65096

Summary: E. C. Du Fort and S. P. Frankel [Math. Tables Aids Comput. 7, 136-152 (1953; Zbl 0053.26401)] proposed to solve the heat equation \(u_t=u_{xx}\) using an explicit scheme, which they claim to be unconditionally stable, with a truncation error is of order of \(\tau= O(k^2+h^2+\frac{{k}^{2}}{{h}^{2}})\). Therefore, it is not consistent when \(k=O(h)\).
In the analysis presented below we show that the Du Fort-Frankel schemes are not unconditionally stable. However, when properly defined, the truncation error vanishes as \(h,k\rightarrow 0\).

MSC:

65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs

Citations:

Zbl 0053.26401
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References:

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