120,209 research outputs found
Numerical integration of an age-structured population model with infinite life span
Producción CientíficaThe choice of age as a physiological parameter to structure a population and to describe its dynamics involves the election of the life-span. The analysis of an unbounded life-span age-structured population model is motivated because, not only new models continue to appear in this framework, but also it is required by the study of the asymptotic behaviour of its dynamics. The numerical integration of the corresponding model is usually performed in bounded domains through the truncation of the age life-span. Here, we propose a new numerical method that avoids the truncation of the unbounded age domain. It is completely analyzed and second order of convergence is established. We report some experiments to exhibit numerically the theoretical results and the behaviour of the problem in the simulation of the evolution of the Nicholson’s blowflies model.Ministerio de Economía, Industria y Competitividad - Fondo Europeo de Desarrollo Regional (project MTM2017-85476-C2-1-P)Ministerio de Ciencia, Innovación y Universidades - Agencia Estatal de Investigación (grants PID2020-113554GB-I00/AEI/10.13039/501100011033 and RED2018-102650-T)Junta de Castilla y Leon - Fondo Europeo de Desarrollo Regional (grant VA193P20)Junta de Castilla y León (grant VA138G18
QCD Calculations by Numerical Integration
Calculations of observables in Quantum Chromodynamics are typically performed
using a method that combines numerical integrations over the momenta of final
state particles with analytical integrations over the momenta of virtual
particles. I discuss a method for performing all of the integrations
numerically.Comment: 9 pages including 2 figures. RevTe
Numerical integration of variational equations
We present and compare different numerical schemes for the integration of the
variational equations of autonomous Hamiltonian systems whose kinetic energy is
quadratic in the generalized momenta and whose potential is a function of the
generalized positions. We apply these techniques to Hamiltonian systems of
various degrees of freedom, and investigate their efficiency in accurately
reproducing well-known properties of chaos indicators like the Lyapunov
Characteristic Exponents (LCEs) and the Generalized Alignment Indices (GALIs).
We find that the best numerical performance is exhibited by the
\textit{`tangent map (TM) method'}, a scheme based on symplectic integration
techniques which proves to be optimal in speed and accuracy. According to this
method, a symplectic integrator is used to approximate the solution of the
Hamilton's equations of motion by the repeated action of a symplectic map ,
while the corresponding tangent map , is used for the integration of the
variational equations. A simple and systematic technique to construct is
also presented.Comment: 27 pages, 11 figures, to appear in Phys. Rev.
Estimating numerical integration errors
Algorithm for use in estimating accumulated numerical integration error
Self-starting procedure simplifies numerical integration
A self-starting, multistep procedure for the numerical integration of ordinary differential equations is devised to produce all the required backward differences directly from the initial equations. The self-starting element eliminates nonessential tallying to determine starting values
On the accuracy of the numerical integrals of the newmark’s method for computing inelastic seismic response
The paper proposes an algorithm of the numerical integration with the modal analysis for computing inelastic seismic responses, and furthermore, the accuracy of the numerical integration with the Newmark’s =1/4 method that is most popular in the earthquake engineering is discussed by comparing with the response computed by the proposed method
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