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 228 articles )

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  1. Abdi, A.; Jackiewicz, Z.: Towards a code for nonstiff differential systems based on general linear methods with inherent Runge-Kutta stability (2019)
  2. Malinzi, Joseph; Amima, Innocenter: Mathematical analysis of a tumour-immune interaction model: a moving boundary problem (2019)
  3. Abdi, Ali; Behzad, Batoul: Efficient Nordsieck second derivative general linear methods: construction and implementation (2018)
  4. Abdi, Ali; Hosseini, Seyyed Ahmad: The barycentric rational difference-quadrature scheme for systems of Volterra integro-differential equations (2018)
  5. 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)
  6. 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)
  7. Ansmann, Gerrit: Efficiently and easily integrating differential equations with JiTCODE, JiTCDDE, and JiTCSDE (2018)
  8. Bocher, Philippe; Montijano, Juan I.; Rández, Luis; Van Daele, Marnix: Explicit Runge-Kutta methods for stiff problems with a gap in their eigenvalue spectrum (2018)
  9. Chatterjee, Abhishek; Rodriguez, Adrian; Bowling, Alan: Analytic solution for planar indeterminate impact problems using an energy constraint (2018)
  10. Fernández-Cara, Enrique; Prouvée, Laurent: Optimal control of mathematical models for the radiotherapy of gliomas: the scalar case (2018)
  11. Garon, Elyse M.; Lambers, James V.: Modeling the diffusion of heat energy within composites of homogeneous materials using the uncertainty principle (2018)
  12. Ghahramani, Ebrahim; Arabnejad, Mohammad Hossein; Bensow, Rickard E.: Realizability improvements to a hybrid mixture-bubble model for simulation of cavitating flows (2018)
  13. Hoffman, F.; Gavaghan, D.; Osborne, J.; Barrett, I. P.; You, T.; Ghadially, H.; Sainson, R.; Wilkinson, R. W.; Byrne, Helen M.: A mathematical model of antibody-dependent cellular cytotoxicity (ADCC) (2018)
  14. Howcroft, C.; Cook, R. G.; Neild, S. A.; Lowenberg, M. H.; Cooper, J. E.; Coetzee, E. B.: On the geometrically exact low-order modelling of a flexible beam: formulation and numerical tests (2018)
  15. Huttunen, J. M. J.; Kaipio, J. P.; Haario, H.: Approximation error approach in spatiotemporally chaotic models with application to Kuramoto-Sivashinsky equation (2018)
  16. Ibrahim, Bashar: Mathematical analysis and modeling of DNA segregation mechanisms (2018)
  17. Khan, Mohammad Farhan; Spurgeon, Sarah; von der Haar, Tobias: Origins of robustness in translational control via eukaryotic translation initiation factor (eIF) 2 (2018)
  18. Klinge, Marcel; Weiner, Rüdiger: Strong stability preserving explicit peer methods for discontinuous Galerkin discretizations (2018)
  19. Klinge, Marcel; Weiner, Rüdiger; Podhaisky, Helmut: Optimally zero stable explicit peer methods with variable nodes (2018)
  20. Kopecz, S.; Meister, A.: On order conditions for modified Patankar-Runge-Kutta schemes (2018)

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