Geodesic
Unconditional stability of difference formulas
Applications of Mathematics, Tome 28 (1983) no. 2, pp. 81-90 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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The paper concerns the solution of partial differential equations of evolution type by the finite difference method. The author discusses the general assumptions on the original equation as well as its discretization, which guarantee that the difference scheme is unconditionally stable, i.e. stable without any stability condition for the time-step. A new notion of the $A_n$-acceptability of the integration formula is introduced and examples of such formulas are given. The results can be applied to ordinary differential equations as well.
The paper concerns the solution of partial differential equations of evolution type by the finite difference method. The author discusses the general assumptions on the original equation as well as its discretization, which guarantee that the difference scheme is unconditionally stable, i.e. stable without any stability condition for the time-step. A new notion of the $A_n$-acceptability of the integration formula is introduced and examples of such formulas are given. The results can be applied to ordinary differential equations as well.
DOI : 10.21136/AM.1983.104008
Classification : 34G10, 35G10, 35K25, 65J10, 65L05, 65M10, 65N12
Keywords: unconditional stability; complex Banach space; finite difference method; $k$-step formula 
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     title = {Unconditional stability of difference formulas},
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Roubíček, Tomáš. Unconditional stability of difference formulas. Applications of Mathematics, Tome 28 (1983) no. 2, pp. 81-90. doi: 10.21136/AM.1983.104008

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