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 189 articles )

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  1. Ibrahim, Bashar: Mathematical analysis and modeling of DNA segregation mechanisms (2018)
  2. Kopecz, S.; Meister, A.: On order conditions for modified Patankar-Runge-Kutta schemes (2018)
  3. Famelis, I.Th.; Jackiewicz, Z.: A new approach to the construction of DIMSIMs of high order and stage order (2017)
  4. Quintero, Maria C.; Cordovez, Juan M.: Looking for an efficient and safe hyperthermia therapy: insights from a partial differential equations based model (2017)
  5. Soleimani, Behnam; Knoth, Oswald; Weiner, Rüdiger: IMEX peer methods for fast-wave-slow-wave problems (2017)
  6. Soleimani, Behnam; Weiner, Rüdiger: A class of implicit peer methods for stiff systems (2017)
  7. Weiner, R.; Kulikov, G.Yu.; Beck, S.; Bruder, J.: New third- and fourth-order singly diagonally implicit two-step peer triples with local and global error controls for solving stiff ordinary differential equations (2017)
  8. Zhao, Xiao; Noack, Stephan; Wiechert, Wolfgang; von Lieres, Eric: Dynamic flux balance analysis with nonlinear objective function (2017)
  9. Balajewicz, Maciej; Tezaur, Irina; Dowell, Earl: Minimal subspace rotation on the Stiefel manifold for stabilization and enhancement of projection-based reduced order models for the compressible Navier-Stokes equations (2016)
  10. Conti, R.; Meli, E.; Ridolfi, A.: A full-scale roller-rig for railway vehicles: multibody modelling and Hardware in the Loop architecture (2016)
  11. Corless, Robert M.; Jankowski, Julia E.: Variations on a theme of Euler (2016)
  12. Duch^ene, V.; Israwi, S.; Talhouk, R.: A new class of two-layer Green-Naghdi systems with improved frequency dispersion (2016)
  13. Goulet, D.: Modeling, simulating, and parameter Fitting of biochemical kinetic experiments (2016)
  14. Humbert, T.; Josserand, C.; Touzé, C.; Cadot, O.: Phenomenological model for predicting stationary and non-stationary spectra of wave turbulence in vibrating plates (2016)
  15. Kim, Philsu; Kim, Junghan; Jung, WonKyu; Bu, Sunyoung: An error embedded method based on generalized Chebyshev polynomials (2016)
  16. Kulikov, G.Yu.; Kulikova, M.V.: Estimating the state in stiff continuous-time stochastic systems within extended Kalman filtering (2016)
  17. Kulyamin, Dmitry V.; Dymnikov, Valentin P.: Numerical modelling of coupled neutral atmospheric general circulation and ionosphere D region (2016)
  18. Calvo, M.; Laburta, M.P.; Montijano, J.I.; Rández, L.: Runge-Kutta projection methods with low dispersion and dissipation errors (2015)
  19. Calzada, Juan A.; Obaya, Rafael; Sanz, Ana M.: Continuous separation for monotone skew-product semiflows: from theoretical to numerical results (2015)
  20. Chalishajar, Dimplekumar; Chalishajar, Heena: Trajectory controllability of second order nonlinear integro-differential system: an analytical and a numerical estimation (2015)

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