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Numerical optimization of parameters in systems of differential equations

Martínek, Josef, Kučera, Václav (2023)

Programs and Algorithms of Numerical Mathematics

We present results on the estimation of unknown parameters in systems of ordinary differential equations in order to fit the output of models to real data. The numerical method is based on the nonlinear least squares problem along with the solution of sensitivity equations corresponding to the differential equations. We will present the performance of the method on the problem of fitting the output of basic compartmental epidemic models to data from the Covid-19 epidemic. This allows us to draw...

Numerical Solution of Bifurcation Problems for Ordinary Differential Equations.

W.F. Langford (1977)

Numerische Mathematik

Numerical Solution of Delay Differential Equations by Uniform Corrections to an Implicit Runge-Kutta Method.

Marino Zennaro, Alfredo Bellen (1985)

Numerische Mathematik

Numerical solution of differential-algebraic equations for constrained mechanical motion.

C. Führer, B.J. Leimkuhler (1991)

Numerische Mathematik

Numerical solution of initial and singularly perturbed two-point boundary value problems using adaptive spline function approximation.

Stojanović, Mirjana (1988)

Publications de l'Institut Mathématique. Nouvelle Série

Numerical Solution of Ordinary and Retarded Differential Equations with Discontinuous Derivatives.

Alan Feldstein, Richard Goodman (1973)

Numerische Mathematik

Numerical Solution of Retarded Initial Value Problems: Local and Global Error and Stepsize Control.

Herbert Arndt (1984)

Numerische Mathematik

Numerical solution of some iterative differential equation

Jiří Kobza (1998)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

Numerical solution of the Maxwell equations in time-varying media using Magnus expansion

István Faragó, Ágnes Havasi, Robert Horváth (2012)

Open Mathematics

For the Maxwell equations in time-dependent media only finite difference schemes with time-dependent conductivity are known. In this paper we present a numerical scheme based on the Magnus expansion and operator splitting that can handle time-dependent permeability and permittivity too. We demonstrate our results with numerical tests.