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 159 articles )

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  2. Kulikov, G.Yu.; Kulikova, M.V.: Estimating the state in stiff continuous-time stochastic systems within extended Kalman filtering (2016)
  3. Kulyamin, Dmitry V.; Dymnikov, Valentin P.: Numerical modelling of coupled neutral atmospheric general circulation and ionosphere D region (2016)
  4. Calvo, M.; Laburta, M.P.; Montijano, J.I.; Rández, L.: Runge-Kutta projection methods with low dispersion and dissipation errors (2015)
  5. Chalishajar, Dimplekumar; Chalishajar, Heena: Trajectory controllability of second order nonlinear integro-differential system: an analytical and a numerical estimation (2015)
  6. Gaudreau, P.; Hayami, K.; Aoki, Y.; Safouhi, H.; Konagaya, A.: Improvements to the cluster Newton method for underdetermined inverse problems (2015)
  7. Johnston, Stuart T.; Simpson, Matthew J.; Baker, Ruth E.: Modelling the movement of interacting cell populations: a moment dynamics approach (2015)
  8. Khuvis, Samuel; Gobbert, Matthias K.; Peercy, Bradford E.: Time-stepping techniques to enable the simulation of bursting behavior in a physiologically realistic computational islet (2015)
  9. Kulikov, G.Yu.; Weiner, R.: A singly diagonally implicit two-step peer triple with global error control for stiff ordinary differential equations (2015)
  10. Nance, J.; Kelley, C.T.: A sparse interpolation algorithm for dynamical simulations in computational chemistry (2015)
  11. Rossides, Tasos; Lloyd, David J.B.; Zelik, Sergey: Computing interacting multi-fronts in one dimensional real Ginzburg Landau equations (2015)
  12. Tiago, Jorge: Numerical simulations for the stabilization and estimation problem of a semilinear partial differential equation (2015)
  13. Wei, Jiamin; Yu, Yongguang; Wang, Sha: Parameter estimation for noisy chaotic systems based on an improved particle swarm optimization algorithm (2015)
  14. Anguelov, R.; Dumont, Y.; Lubuma, J.M.-S.; Shillor, M.: Dynamically consistent nonstandard finite difference schemes for epidemiological models (2014)
  15. Bradley, Ben K.; Jones, Brandon A.; Beylkin, Gregory; Sandberg, Kristian; Axelrad, Penina: Bandlimited implicit Runge-Kutta integration for astrodynamics (2014)
  16. Duch^ene, Vincent: On the rigid-lid approximation for two shallow layers of immiscible fluids with small density contrast (2014)
  17. Duque, José C.M.; Almeida, Rui M.P.; Antontsev, Stanislav N.: Numerical study of the porous medium equation with absorption, variable exponents of nonlinearity and free boundary (2014)
  18. Emelianenko, Maria; Torrejon, Diego; Denardo, Matthew A.; Socolofsky, Annika K.; Ryabov, Alexander D.; Collins, Terrence J.: Estimation of rate constants in nonlinear reactions involving chemical inactivation of oxidation catalysts (2014)
  19. Fernandez-Feria, R.; Ortega-Casanova, J.: A pseudospectral based method of lines for solving integro-differential boundary-layer equations. Application to the mixed convection over a heated horizontal plate (2014)
  20. Jimenez, J.C.; Sotolongo, A.; Sanchez-Bornot, J.M.: Locally linearized Runge Kutta method of Dormand and Prince (2014)

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