ode23

The MATLAB ODE Suite: ode23: Solve nonstiff differential equations; low order method. [T,Y] = solver(odefun,tspan,y0) with tspan = [t0 tf] integrates the system of differential equations y′ = f(t,y) from time t0 to tf with initial conditions y0. The first input argument, odefun, is a function handle. The function, f = odefun(t,y), for a scalar t and a column vector y, must return a column vector f corresponding to f(t,y). Each row in the solution array Y corresponds to a time returned in column vector T. To obtain solutions at the specific times t0, t1,...,tf (all increasing or all decreasing), use tspan = [t0,t1,...,tf]. Parameterizing Functions explains how to provide additional parameters to the function fun, if necessary. [T,Y] = solver(odefun,tspan,y0,options) solves as above with default integration parameters replaced by property values specified in options, an argument created with the odeset function. Commonly used properties include a scalar relative error tolerance RelTol (1e-3 by default) and a vector of absolute error tolerances AbsTol (all components are 1e-6 by default). If certain components of the solution must be nonnegative, use the odeset function to set the NonNegative property to the indices of these components. See odeset for details. [T,Y,TE,YE,IE] = solver(odefun,tspan,y0,options) solves as above while also finding where functions of (t,y), called event functions, are zero. For each event function, you specify whether the integration is to terminate at a zero and whether the direction of the zero crossing matters. Do this by setting the ’Events’ property to a function, e.g., events or @events, and creating a function [value,isterminal,direction] = events(t,y). For the ith event function in events, value(i) is the value of the function. isterminal(i) = 1, if the integration is to terminate at a zero of this event function and 0 otherwise. direction(i) = 0 if all zeros are to be computed (the default), +1 if only the zeros where the event function increases, and -1 if only the zeros where the event function decreases. Corresponding entries in TE, YE, and IE return, respectively, the time at which an event occurs, the solution at the time of the event, and the index i of the event function that vanishes.


References in zbMATH (referenced in 335 articles )

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  1. Abdi, Ali; Hojjati, Gholamreza; Izzo, Giuseppe; Jackiewicz, Zdzislaw: Global error estimation for explicit second derivative general linear methods (2022)
  2. Aoki, Yasunori; Hayami, Ken; Toshimoto, Kota; Sugiyama, Yuichi: Cluster Gauss-Newton method. An algorithm for finding multiple approximate minimisers of nonlinear least squares problems with applications to parameter estimation of pharmacokinetic models (2022)
  3. Apiyo, D.; Mouton, J. M.; Louw, C.; Sampson, S. L.; Louw, T. M.: Dynamic mathematical model development and validation of \textitinvitro Mycobacterium smegmatis growth under nutrient- and pH-stress (2022)
  4. Blühdorn, Johannes; Gauger, Nicolas R.; Kabel, Matthias: AutoMat: automatic differentiation for generalized standard materials on GPUs (2022)
  5. Burkardt, John; Pei, Wenlong; Trenchea, Catalin: A stress test for the midpoint time-stepping method (2022)
  6. Fekete, Imre; Conde, Sidafa; Shadid, John N.: Embedded pairs for optimal explicit strong stability preserving Runge-Kutta methods (2022)
  7. Juma, Victor Ogesa; Dehmelt, Leif; Portet, Stéphanie; Madzvamuse, Anotida: A mathematical analysis of an activator-inhibitor Rho GTPase model (2022)
  8. Nagy, Dániel; Plavecz, Lambert; Hegedűs, Ferenc: The art of solving a large number of non-stiff, low-dimensional ordinary differential equation systems on GPUs and CPUs (2022)
  9. Nasr, Walid W.: Inventory systems with stochastic and batch demand: computational approaches (2022)
  10. Siettos, Constantinos; Russo, Lucia: A numerical method for the approximation of stable and unstable manifolds of microscopic simulators (2022)
  11. Villa, Andrea; Schurch, Roger; Buccella, Giacomo; Barbieri, Luca; Laurano, Christian; Malgesini, Roberto; Palladini, Daniele: Simulation of surface-plasma interaction with high surface conductivity (2022)
  12. Walker, B. J.; Ishimoto, K.; Gaffney, E. A.; Moreau, C.: The control of particles in the Stokes limit (2022)
  13. Yu, Xinxin; Aceituno, Javier F.; Kurvinen, Emil; Matikainen, Marko K.; Korkealaakso, Pasi; Rouvinen, Asko; Jiang, Dezhi; Escalona, José L.; Mikkola, Aki: Comparison of numerical and computational aspects between two constraint-based contact methods in the description of wheel/rail contacts (2022)
  14. Abdi, Ali; Hojjati, Gholamreza: Second derivative backward differentiation formulae for ODEs based on barycentric rational interpolants (2021)
  15. Alì, Giuseppe; Bilotta, Eleonora; Chiaravalloti, Francesco; Pantano, Pietro; Pezzi, Oreste; Scuro, Carmelo; Valentini, Francesco: Spatiotemporal pattern formation in a ring of Chua’s oscillators (2021)
  16. Ávila, Andrés I.; González, Galo Javier; Kopecz, Stefan; Meister, Andreas: Extension of modified Patankar-Runge-Kutta schemes to nonautonomous production-destruction systems based on Oliver’s approach (2021)
  17. Borges, J. S.; Ferreira, J. A.; Romanazzi, G.; Abreu, E.: Drug release from viscoelastic polymeric matrices -- a stable and supraconvergent FDM (2021)
  18. Chatterjee, Abhishek; Ghaednia, Hamid; Bowling, Alan; Brake, Matthew: Estimation of impact forces during multi-point collisions involving small deformations (2021)
  19. Coskun, Erhan: On the properties of a single vortex solution of Ginzburg-Landau model of superconductivity (2021)
  20. Debrabant, Kristian; Kværnø, Anne; Mattsson, Nicky Cordua: Runge-Kutta Lawson schemes for stochastic differential equations (2021)

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Further publications can be found at: http://epubs.siam.org/doi/abs/10.1137/S1064827594276424