Optimization-based search for nordsieck methods of high order with quadratic stability polynomials
Mathematical Modelling and Analysis, 2012 We describe the search for explicit general linear methods in Nordsieck form for which the stability function has only two nonzero roots. This search is based on state-of-the-art optimization software.
Angelamaria Cardone +2 more
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The Z5 transformation for solving quasi-linear partial differential equations
Partial Differential Equations in Applied Mathematics, 2023 The Z1-Z4 transformations proposed in our previous papers have acquired remarkable success in the field of linear partial differential equations, general solutions of a large number of typical equations were obtained for the first time, and exact ...
Hong Lai Zhu
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Numerical Methods for Ill-Posed, Linear Problems [PDF]
, 1975 A means of assessing the effectiveness of methods used in the numerical solution of various linear ill-posed problems is outlined. Two methods: Tikhonov' s method of regularization and the quasireversibility method of Lattès and Lions are appraised from ...
Stevens, Thomas
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A practical approach for the derivation of algebraically stable two-step Runge-Kutta methods
Mathematical Modelling and Analysis, 2012 We describe an algorithm, based on a new strategy recently proposed by Hewitt and Hill in the context of general linear methods, for the construction of algebraically stable two-step Runge-Kutta methods.
Dajana Conte +3 more
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Strong Stability Preserving Multistage Integration Methods
Mathematical Modelling and Analysis, 2015 In this paper we systematically investigate explicit strong stability preserving (SSP) multistage integration methods, a subclass of general linear methods (GLMs), of order p and stage order q ≤ p.
Giuseppe Izzo, Zdzislaw Jackiewicz
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Construction of Nordsieck Second Derivative General Linear Methods with Inherent Quadratic Stability
Mathematical Modelling and Analysis, 2017 This paper describes the construction of second derivative general linear methods in Nordsieck form with stability properties determined by quadratic stability functions. This is achieved by imposing the so–called inherent quadratic stability conditions.
Akram Movahedinejad +2 more
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Some efficient Nordsieck integration methods for IVPs [PDF]
Iranian Journal of Numerical Analysis and Optimization, 2018 In this paper, in continuation of the construction of efficient numerical methods for stiff IVPs, we construct type two Nordsieck second derivative general linear methods with order p = s, where s is the number of internal stages, and stage order q = p ...
N. Barghi Oskouie, A. Abdi, G. Hojjati
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Linear stationary iterative methods for the force-based quasicontinuum approximation [PDF]
, 2012 Force-based multiphysics coupling methods have become popular since they provide a simple and efficient coupling mechanism, avoiding the difficulties in formulating and implementing a consistent coupling energy.
Luskin, Mitchell Barry +1 more
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Global error estimation for explicit second derivative general linear methods [PDF]
, 2022 In this paper, we describe an approach to estimate the global error for explicit second derivative general linear methods based on the approach which has been already used for global error estimation of explicit general linear methods.
Izzo G. +3 more
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Genotype Selection for Grain Yield of Sorghum through Generalized Linear Mixed Model
Agronomy, 2023 The classical model only provides a correct analysis if all the effects are fixed. For experiments that include fixed and random effects, the general linear mixed model is appropriate for handling the non-normal distributed response variables. The aim of
Mulugeta Tesfa +4 more
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