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. Lamba, Harbir; Stuart, Andrew: Convergence proofs for numerical IVP software (2000)
  2. Shampine, L. F.; Corless, Robert M.: Initial value problems for ODEs in problem solving environments (2000)
  3. Shampine, L. F.; Thompson, S.: Event location for ordinary differential equations (2000)
  4. Hall, George; Usman, Anila: Modified order and stepsize strategies in Adams codes (1999)
  5. Shampine, L. F.: Conservation laws and the numerical solution of ODEs. II (1999)
  6. Brugnano, Luigi; Trigiante, Donato: Parallel implementation of block boundary value methods on nonlinear problems: Theoretical results (1998)
  7. Higham, D. J.; Stuart, A. M.: Analysis of the dynamics of local error control via a piecewise continuous residual (1998)
  8. Lamba, H.; Stuart, A. M.: Convergence results for the MATLAB ode23 routine (1998)
  9. Shampine, L. F.: Linear conservation laws for ODEs (1998)
  10. Simeon, B.: Stiff solvers and model reduction in flexible multibody systems (1998)
  11. Wain, Richard J.: Spurios fixed points of a variable step size, variable order, predictor corrector algorithm (1998)
  12. Ahmad, I.; Berzins, M.: An algorithm for ODEs from atmospheric dispersion problems (1997)
  13. Günther, M.; Hoschek, M.: ROW methods adapted to electric circuit simulation packages (1997)
  14. Muraca, P.; Pugliese, P.: A variable-structure regulator for robotic systems (1997)
  15. Shampine, Lawrence F.; Reichelt, Mark W.: The MATLAB ODE suite (1997)
  16. Hosea, M. E.; Shampine, L. F.: Analysis and implementation of TR-BDF2 (1996)
  17. Shampine, L. F.; Gladwell, I.: Software based on explicit RK formulas (1996)
  18. Piché, Robert: An (L)-stable Rosenbrock method for step-by-step time integration in structural dynamics. (1995)

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