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. Stemp, Peter J.; Herbert, Ric D: Solving non-linear models with saddle-path instabilities (2006)
  2. Thompson, S.; Shampine, L. F.: A friendly Fortran DDE solver (2006)
  3. Trendafilov, Nickolay T.; Jolliffe, Ian T.: Projected gradient approach to the numerical solution of the SCoTLASS (2006)
  4. Bartoszewski, Z.; Jackiewicz, Z.: Nordsieck representation of two-step Runge-Kutta methods for ordinary differential equations (2005)
  5. Garay, Barnabas M.; Lee, Keonhee: Attractors under discretizations with variable stepsize (2005)
  6. Lamba, Harbir: The effective stability of adaptive timestepping ODE solvers (2005)
  7. Locke, J. C. W.; Millar, A. J.; Turner, M. S.: Modelling genetic networks with noisy and varied experimental data: the circadian clock in \textitArabidopsisthaliana (2005)
  8. Shampine, L. F.; Thompson, S.; Kierzenka, J. A.; Byrne, G. D.: Nonnegative solutions of ODEs (2005)
  9. Soane, Ana Maria; Gobbert, Matthias K.; Seidman, Thomas I.: Numerical exploration of a system of reaction-diffusion equations with internal and transient layers (2005)
  10. Vanroyen, Claude; Omari, Abdelaziz; Toutain, Jean; Reungoat, David: Interactions between hard spheres sedimenting at low Reynolds number (2005)
  11. Bause, Markus; Knabner, Peter: Numerical simulation of contaminant biodegradation by higher order methods and adaptive time stepping (2004)
  12. Causin, Paola; Restelli, Marco; Sacco, Riccardo: A simulation system based on mixed-hybrid finite elements for thermal oxidation in semiconductor technology (2004)
  13. Chu, Moody T.; Diele, Fasma; Sgura, Ivonne: Gradient flow methods for matrix completion with prescribed eigenvalues. (2004)
  14. Hanhart, Alexander L.; Gobbert, Matthias K.; Izu, Leighton T.: A memory-efficient finite element method for systems of reaction--diffusion equations with non-smooth forcing (2004)
  15. Konagaya, Akihiko; Konishi, Fumikazu; Hatakeyama, Mariko; Satou, Kenji: The superstructure toward open bioinformatics grid (2004)
  16. Ropp, David L.; Shadid, John N.; Ober, Curtis C.: Studies of the accuracy of time integration methods for reaction-diffusion equations. (2004)
  17. Sapariuc, I.; Marcozzi, M. D.; Flaherty, J. E.: A numerical analysis of variational valuation techniques for derivative securities (2004)
  18. Voss, D. A.: Fourth-order parallel Rosenbrock formulae for stiff systems (2004)
  19. Caraballo, T.; Marín-Rubio, P.; Robinson, J. C.: A comparison between two theories for multi-valued semiflows and their asymptotic behaviour (2003)
  20. Chollom, J.; Jackiewicz, Z.: Construction of two-step Runge--Kutta methods with large regions of absolute stability (2003)

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