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 $S$, while the corresponding tangent map $TS$, is used for the integration of the variational equations. A simple and systematic technique to construct $TS$ 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