Documents published in Scipedia

• Parameter estimation in ODEs. Modelling and computational issues

  L. Juárez Valencia, J. ROJAS

  SMCCA (2022). 2

  
  

  Abstract

  In this work we discuss a variational approach for the determination of the parameters of systems of ordinary differential equations (ODE). We construct a model for fitting observed noisy data into the given dynamical system. Also we explain in detail the advantage of using the adjoint equation method to compute the derivatives or gradients, which are needed for the application of gradient methods and quasi-Newton algorithms to find the minimum of the cost function. In particular we consider two classic iterative algorithms: the conjugate gradient (CG) algorithm and the BFGS algorithm. For educational purposes we try to explain several numerical and computational issues with some detail and illustrate them with the SEIRD epidemiological model.

  Abstract
  In this work we discuss a variational approach for the determination of the parameters of systems of ordinary differential equations (ODE). We construct a model for fitting [...]

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• Stabilizing a Josephson Junction Array Memory around an unstable equilibrium: A control approach using a first order state model

  J. LOPEZ, L. Juárez Valencia, R. Glowinski

  SMCCA (2022). 1

  
  

  Abstract

  In this paper we consider a system of three nonlinear ordinary differential equations that model a three Josephson Junctions Array (JJA). Our goal is to stabilize the system around an unstable equilibrium employing an optimal control approach. We first define the cost functional and calculate its differential by using perturbation analysis and variational calculus. For the computational solution of the optimality system we consider a conjugate gradient algorithm for quadratic functionals in Hilbert spaces,  combined with a finite difference discretization of the involucrated differential equations.

  Abstract
  In this paper we consider a system of three nonlinear ordinary differential equations that model a three Josephson Junctions Array (JJA). Our goal is to stabilize the system [...]

  • 18
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