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 318 articles )

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  1. Daniels, P. G.; Ho, D.; Skeldon, A. C.: Solutions for nonlinear convection in the presence of a lateral boundary (2003)
  2. Kelley, C. T.; Sachs, E. W.: Truncated Newton methods for optimization with inaccurate functions and gradients (2003)
  3. Lin, Juan; Andreasen, Viggo; Casagrandi, Renato; A. Levin, Simon: Traveling waves in a model of influenza A drift (2003)
  4. Moon, Kyoung-Sook; Szepessy, Anders; Tempone, Raúl; Zouraris, Georgios E.: Convergence rates for adaptive approximation of ordinary differential equations (2003)
  5. Shampine, L. F.: Singular boundary value problems for ODEs (2003)
  6. Bartel, Andreas; Günther, Michael: A multirate W-method for electrical networks in state-space formulation (2002)
  7. deMello, J. C.: Highly convergent simulations of transport dynamics in organic light-emitting diodes (2002)
  8. Grüne, Lars: Asymptotic behavior of dynamical and control systems under perturbation and discretization (2002)
  9. Jackiewicz, Z.: Implementation of DIMSIMs for stiff differential systems (2002)
  10. Shampine, L. F.: Variable order Adams codes. (2002)
  11. Trendafilov, Nickolay T.; Lippert, Ross A.: The multimode Procrustes problem (2002)
  12. Banks, H. T.; Musante, C. J.; Raye, J. K.: Predictions for a distributed parameter model decribing the hepatic processing of 2,3,7,8-TCDD (2001)
  13. Bartel, Andreas; Günther, Michael: Developments in multirating for coupled systems (2001)
  14. de Pillis, E. G.; de Pillis, L. G.: The long-term impact of university budget cuts: A mathematical model (2001)
  15. Duncan, Dugald B.; Soheili, Ali R.: Approximating the Becker-Döring cluster equations (2001)
  16. Judd, Kevin; Smith, Leonard: Indistinguishable states. I: Pefect model scenario. (2001)
  17. Sanchirico, James N.; Wilen, James E.: Dynamics of spatial exploitation: A metapopulation approach (2001)
  18. Shampine, L. F.; Thompson, S.: Solving DDEs in Matlab (2001)
  19. Ashino, R.; Nagase, M.; Vaillancourt, R.: Behind and beyond the MATLAB ODE suite (2000)
  20. Lamba, H.: Dynamical systems and adaptive timestepping in ODE solvers (2000)

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