scholarly journals Efficient method for solving highly oscillatory ordinary differential equations with applications to physical systems

2020 ◽  
Vol 2 (1) ◽  
Author(s):  
F. J. Agocs ◽  
W. J. Handley ◽  
A. N. Lasenby ◽  
M. P. Hobson
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Efficient Method ◽  
Physical Systems ◽  
Highly Oscillatory

A Method to Find Non-Zero Operating Point Volterra Models for Port-Based Ordinary Differential Equations

2010 ◽  
Author(s):  
Eliot Motato ◽  
Clark Radcliffe ◽  
Jose Luis Viveros
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Transfer Functions ◽  
Operating Conditions ◽  
Operating Point ◽  
Input Output ◽  
Nonlinear Functions ◽  
Nonlinear Odes ◽  
Physical Systems ◽  
Volterra Models

Nonlinear physical systems frequently perform around constant non-zero input-output operating conditions. This local behavior can be modeled using port-based nonlinear ordinary differential equations (ODEs). An ODE local solution around an specific input-output operating point can be obtained through the Volterra transfer function (VTF) model. In a past work a procedure for obtaining MIMO Volterra models from port-based nonlinear ODEs was presented. This previous work considered only systems operating at zero input-output conditions subject to linear inputs. In this work the process for obtaining MIMO Volterra transfer functions is extended for systems operating at non-zero input-output conditions. This extension also allows systems that are nonlinear functions of their inputs and input derivatives.

Numerical solution of highly oscillatory ordinary differential equations

Acta Numerica ◽  
1997 ◽  
Vol 6 ◽  
pp. 437-483 ◽  
Author(s):  
Linda R. Petzold ◽  
Laurent O. Jay ◽  
Jeng Yen
Keyword(s):  
Differential Equations ◽  
Numerical Solution ◽  
Ordinary Differential Equations ◽  
Structural Model ◽  
Circuit Simulation ◽  
Differential Algebraic Equations ◽  
Algebraic Equations ◽  
Vehicle Simulation ◽  
Oscillatory Systems ◽  
Highly Oscillatory

One of the most difficult problems in the numerical solution of ordinary differential equations (ODEs) and in differential-algebraic equations (DAEs) is the development of methods for dealing with highly oscillatory systems. These types of systems arise, for example, in vehicle simulation when modelling the suspension system or tyres, in models for contact and impact, in flexible body simulation from vibrations in the structural model, in molecular dynamics, in orbital mechanics, and in circuit simulation. Standard numerical methods can require a huge number of time-steps to track the oscillations, and even with small stepsizes they can alter the dynamics, unless the method is chosen very carefully.

scholarly journals Parameter Estimation in Ordinary Differential Equations Modeling via Particle Swarm Optimization

2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Devin Akman ◽  
Olcay Akman ◽  
Elsa Schaefer
Keyword(s):  
Parameter Estimation ◽  
Particle Swarm Optimization ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Efficient Method ◽  
Epidemic Model ◽  
Particle Swarm ◽  
Computing Methods ◽  
Swarm Optimization ◽  
Computationally Expensive

Researchers using ordinary differential equations to model phenomena face two main challenges among others: implementing the appropriate model and optimizing the parameters of the selected model. The latter often proves difficult or computationally expensive. Here, we implement Particle Swarm Optimization, which draws inspiration from the optimizing behavior of insect swarms in nature, as it is a simple and efficient method for fitting models to data. We demonstrate its efficacy by showing that it outstrips evolutionary computing methods previously used to analyze an epidemic model.

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