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Computers and Mathematics With Applications, 1996 General linear methods, as multistage multivalue methods, are the natural generalizations of linear multistep and Runge-Kutta methods. This survey contains a discussion of the traditional methods and a motivation for the general linear type of generalization.
J C Butcher
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General linear methods for Volterra integral equations
Journal of Computational and Applied Mathematics, 2010 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Giuseppe Izzo +2 more
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High order second derivative diagonally implicit multistage integration methods for ODEs
Mathematical Modelling and Analysis, 2023 Construction of second derivative diagonally implicit multistage integration methods (SDIMSIMs) as a subclass of second derivative general linear methods with Runge–Kutta stability property requires to generate the corresponding conditions depending of ...
Mohammad Sharifi +3 more
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A General Multibody Approach for the Linear and Nonlinear Stability Analysis of Bicycle Systems. Part I: Methods of Constrained Dynamics [PDF]
Journal of Applied and Computational Mechanics, 2021 This investigation is the first contribution of a two-part research work concerning the theoretical development of a multibody approach to analyze the constrained dynamics of articulated mechanical systems.
Carmine Maria Pappalardo +2 more
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High order second derivative methods with Runge--Kutta stability for the numerical solution of stiff ODEs [PDF]
Iranian Journal of Numerical Analysis and Optimization, 2015 We describe the construction of second derivative general linear methods (SGLMs) of orders five and six. We will aim for methods which are A--stable and have Runge--Kutta stability property. Some numerical results are given to show the efficiency of
Ali Abdi, Gholamreza Hojjati
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Approximate controllability of second order infinite dimensional systems [PDF]
Archives of Control Sciences, 2021 In the paper approximate controllability of second order infinite dimensional system with damping is considered. Applying linear operators in Hilbert spaces general mathematical model of second order dynamical systems with damping is presented.
Jerzy Klamka, Asatur Zh. Khurshudyan
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Numerical solution of stiff systems of differential equations arising from chemical reactions [PDF]
Iranian Journal of Numerical Analysis and Optimization, 2014 Long time integration of large stiff systems of initial value problems, arising from chemical reactions, demands efficient methods with good accuracy and extensive absolute stability region.
Gholamreza Hojjati +3 more
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Parallel Implicit-Explicit General Linear Methods [PDF]
Communications on Applied Mathematics and Computation, 2020 High-order discretizations of partial differential equations (PDEs) necessitate high-order time integration schemes capable of handling both stiff and nonstiff operators in an efficient manner. Implicit-explicit (IMEX) integration based on general linear methods (GLMs) offers an attractive solution due to their high stage and method order, as well as ...
Steven Roberts +2 more
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Second derivative General Linear Method in Nordsieck form
Journal of Numerical Analysis and Approximation Theory, 2019 This paper considers the construction of second derivative general linear methods (SD-GLM) from hybrid LMM and their transformation to Nordsieck GLM. How the Runge-Kutta starters for the methods can be derived are given.
Robert I. Okuonghae +1 more
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Efficient General Linear Methods of High Order with Inherent Quadratic Stability
Mathematical Modelling and Analysis, 2014 We search for general linear methods with s internal stages and r = s + 1 external stages of order p = s + 1 and stage order q = s. We require that stability function of these methods has only two non-zero roots.
Michal Bras, Zdzislaw Jackiewicz
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