Numerical methods for solving large-scale systems of differential equations

2021 ◽  
Author(s):  
Lakhlifa Sadek ◽  
Hamad Talibi Alaoui
Keyword(s):  
Numerical Methods ◽  
Differential Equations ◽  
Large Scale ◽  
Large Scale Systems ◽  
Systems Of Differential Equations

scholarly journals A PARALLEL MULTIRATE ALGORITHM FOR THE NUMERICAL INTEGRATION OF SYSTEM OF NONLINEAR DIFFERENTIAL EQUATIONS

2014 ◽  
pp. 34-41
Author(s):  
Petro Stakhiv ◽  
Serhiy Rendzinyak
Keyword(s):  
Differential Equations ◽  
Numerical Integration ◽  
Dynamic Behavior ◽  
Large Scale ◽  
Nonlinear Differential Equations ◽  
New Approach ◽  
Large Scale Systems ◽  
Computing Process ◽  
Parallelization Efficiency

The new approach to calculate dynamic behavior of large-scale systems, separated on subsystems is presented. Parallelization efficiency of computing process is described.

scholarly journals Effective numerical methods to model dynamic behavior of springs with torsion

2018 ◽  
Author(s):  
◽  
E. Dilan Fernando
Keyword(s):  
Numerical Methods ◽  
Differential Equations ◽  
Numerical Method ◽  
Dynamic Behavior ◽  
Numerical Models ◽  
Software Implementation ◽  
Computer Language ◽  
Newtonian Mechanics ◽  
Systems Of Differential Equations ◽  
Kirchhoff Problem

The purpose of this thesis is to find effective algorithms to numerically solve certain systems of differential equations that arise from standard Newtonian mechanics. Numerical models of elastica has already been well studied. In this thesis we concentrate on the Kirchhoff problem. The goal is to create an effective and robust numerical method to model the dynamic behavior of springs that have a prescribed natural curvature. In addition to the mathematics, we also provide the implementation details of the numerical method using the computer language Python 3. We also discuss in detail the various difficulties of such a software implementation and how certain auxiliary computations can make the software more effective and robust.

scholarly journals Aggregation–decomposition and equi-ultimate boundedness

1975 ◽  
Vol 19 (2) ◽  
pp. 249-258 ◽  
Author(s):  
P. E. Kloeden
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Decomposition Method ◽  
Large Scale ◽  
Nonlinear Ordinary Differential Equations ◽  
Sufficient Condition ◽  
Ultimate Boundedness ◽  
Large Scale Systems

AbstractThe aggregation–decomposition method is used to derive a sufficient condition for the equi-ultimate boundedness of large-scale systems governed by nonlinear ordinary differential equations.

Numerical methods for Kohn–Sham density functional theory

Acta Numerica ◽  
2019 ◽  
Vol 28 ◽  
pp. 405-539 ◽  
Author(s):  
Lin Lin ◽  
Jianfeng Lu ◽  
Lexing Ying
Keyword(s):  
Density Functional Theory ◽  
Numerical Methods ◽  
Density Functional ◽  
Large Scale ◽  
State Of The Art ◽  
Structure Theory ◽  
Significant Progress ◽  
Functional Theory ◽  
Large Scale Systems ◽  
The Past

Kohn–Sham density functional theory (DFT) is the most widely used electronic structure theory. Despite significant progress in the past few decades, the numerical solution of Kohn–Sham DFT problems remains challenging, especially for large-scale systems. In this paper we review the basics as well as state-of-the-art numerical methods, and focus on the unique numerical challenges of DFT.

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