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Subjects
65-XX Numerical analysis
65Dxx Numerical approximation and computational geometry (primarily algorithms)
65D25 Numerical differentiation

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Comparison of explicit and implicit difference schemes for parabolic functional differential equations

Zdzisław Kamont, Karolina Kropielnicka (2012)

Annales Polonici Mathematici

Initial-boundary value problems of Dirichlet type for parabolic functional differential equations are considered. Explicit difference schemes of Euler type and implicit difference methods are investigated. The following theoretical aspects of the methods are presented. Sufficient conditions for the convergence of approximate solutions are given and comparisons of the methods are presented. It is proved that the assumptions on the regularity of the given functions are the same for both methods. It...

Complexity of the method of averaging

Dalík, Josef (2010)

Programs and Algorithms of Numerical Mathematics

The general method of averaging for the superapproximation of an arbitrary partial derivative of a smooth function in a vertex $a$ of a simplicial triangulation $𝒯$ of a bounded polytopic domain in $ℜ^{d}$ for any $d \geq 2$ is described and its complexity is analysed.

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