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Zero Dissipative DIRKN Pairs of Order 5(4) for Solving Special Second Order IVPs

S. O. Imoni, M. N. O. Ikhile (2014)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

For initial value problem (IVPs) in ordinary second order differential equations of the special form y ' ' = f x , y possessing oscillating solutions, diagonally implicit Runge–Kutta–Nystrom (DIRKN) formula-pairs of orders 5(4) in 5-stages are derived in this paper. The method is zero dissipative, thus it possesses a non-empty interval of periodicity. Some numerical results are presented to show the applicability of the new method compared with existing Runge–Kutta (RK) method applied to the problem reduced to...

Zero points of quadratic matrix polynomials

Opfer, Gerhard, Janovská, Drahoslava (2013)

Applications of Mathematics 2013

Our aim is to classify and compute zeros of the quadratic two sided matrix polynomials, i.e. quadratic polynomials whose matrix coefficients are located at both sides of the powers of the matrix variable. We suppose that there are no multiple terms of the same degree in the polynomial 𝐩 , i.e., the terms have the form 𝐀 j 𝐗 j 𝐁 j , where all quantities 𝐗 , 𝐀 j , 𝐁 j , j = 0 , 1 , ... , N , are square matrices of the same size. Both for classification and computation, the essential tool is the description of the polynomial 𝐩 by a matrix equation...

Zienkiewicz–Zhu error estimators on anisotropic tetrahedral and triangular finite element meshes

Gerd Kunert, Serge Nicaise (2003)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

We consider a posteriori error estimators that can be applied to anisotropic tetrahedral finite element meshes, i.e. meshes where the aspect ratio of the elements can be arbitrarily large. Two kinds of Zienkiewicz–Zhu (ZZ) type error estimators are derived which originate from different backgrounds. In the course of the analysis, the first estimator turns out to be a special case of the second one, and both estimators can be expressed using some recovered gradient. The advantage of keeping two different...

Zienkiewicz–Zhu error estimators on anisotropic tetrahedral and triangular finite element meshes

Gerd Kunert, Serge Nicaise (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We consider a posteriori error estimators that can be applied to anisotropic tetrahedral finite element meshes, i.e. meshes where the aspect ratio of the elements can be arbitrarily large. Two kinds of Zienkiewicz–Zhu (ZZ) type error estimators are derived which originate from different backgrounds. In the course of the analysis, the first estimator turns out to be a special case of the second one, and both estimators can be expressed using some recovered gradient. The advantage of keeping two...

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