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 251 articles )

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  1. Abdi, Ali; Hojjati, Gholamreza: Projection of second derivative methods for ordinary differential equations with invariants (2020)
  2. Gzal, Majdi; Gendelman, O. V.: Edge states and frequency response in nonlinear forced-damped model of valve spring (2020)
  3. Suarez, Gonzalo P.; Udiani, Oyita; Allan, Brian F.; Price, Candice; Ryan, Sadie J.; Lofgren, Eric; Coman, Alin; Stone, Chris M.; Gallos, Lazaros K.; Fefferman, Nina H.: A generic arboviral model framework for exploring trade-offs between vector control and environmental concerns (2020)
  4. Abdi, A.; Jackiewicz, Z.: Towards a code for nonstiff differential systems based on general linear methods with inherent Runge-Kutta stability (2019)
  5. Belov, A. A.; Kalitkin, N. N.: Efficient numerical integration methods for the Cauchy problem for stiff systems of ordinary differential equations (2019)
  6. Bhatoo, Omishwary; Peer, Arshad Ahmud Iqbal; Tadmor, Eitan; Tangman, Désiré Yannick; Saib, Aslam Aly El Faidal: Conservative third-order central-upwind schemes for option pricing problems (2019)
  7. Curry, Charles; Owren, Brynjulf: Variable step size commutator free Lie group integrators (2019)
  8. Jenkins, Luke T.; Foschi, Martino; MacMinn, Christopher W.: Impact of pressure dissipation on fluid injection into layered aquifers (2019)
  9. Keshavarzzadeh, Vahid; Kirby, Robert M.; Narayan, Akil: Convergence acceleration for time-dependent parametric multifidelity models (2019)
  10. Kirkinis, E.; Andreev, A. V.: Healing of thermocapillary film rupture by viscous heating (2019)
  11. Maestrini, Davide; Salman, Hayder: Entropy of negative temperature states for a point vortex gas (2019)
  12. Malinzi, Joseph; Amima, Innocenter: Mathematical analysis of a tumour-immune interaction model: a moving boundary problem (2019)
  13. Montijano, J. I.; Podhaisky, H.; Rández, L.; Calvo, M.: A family of (L)-stable singly implicit peer methods for solving stiff IVPs (2019)
  14. Singh, Gurjinder; Garg, Arvind; Kanwar, V.; Ramos, Higinio: An efficient optimized adaptive step-size hybrid block method for integrating differential systems (2019)
  15. Sulman, M.; Nguyen, T.: A positivity preserving adaptive moving mesh method for cancer cell invasion models (2019)
  16. Abdi, Ali; Behzad, Batoul: Efficient Nordsieck second derivative general linear methods: construction and implementation (2018)
  17. Abdi, Ali; Hosseini, Seyyed Ahmad: The barycentric rational difference-quadrature scheme for systems of Volterra integro-differential equations (2018)
  18. Al Marzooq, Sadiqah; Ortiz-Lugo, Alvaro; Vaughan, Benjamin L. jun.: Mathematical model of biofilm-mediated pathogen persistence in a water distribution network with time-constant flows (2018)
  19. Angiulli, Giovanni; Jannelli, Alessandra; Morabito, F. Carlo; Versaci, Mario: Reconstructing the membrane detection of a 1D electrostatic-driven MEMS device by the shooting method: convergence analysis and ghost solutions identification (2018)
  20. Ansmann, Gerrit: Efficiently and easily integrating differential equations with JiTCODE, JiTCDDE, and JiTCSDE (2018)

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