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 279 articles )

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  1. Iavernaro, F.; Mazzia, F.; Mukhametzhanov, M. S.; Sergeyev, Ya. D.: Computation of higher order Lie derivatives on the infinity computer (2021)
  2. Abdi, Ali; Conte, Dajana: Implementation of second derivative general linear methods (2020)
  3. Abdi, Ali; Hojjati, Gholamreza: Projection of second derivative methods for ordinary differential equations with invariants (2020)
  4. Abdi, Ali; Hojjati, Gholamreza; Sharifi, Mohammad: Implicit-explicit second derivative diagonally implicit multistage integration methods (2020)
  5. Christov, Ivan C.; Ibraguimov, Akif; Islam, Rahnuma: Long-time asymptotics of non-degenerate non-linear diffusion equations (2020)
  6. Diniz-Ehrhardt, M. A.; Ferreira, D. G.; Santos, S. A.: Applying the pattern search implicit filtering algorithm for solving a noisy problem of parameter identification (2020)
  7. Gzal, Majdi; Gendelman, O. V.: Edge states and frequency response in nonlinear forced-damped model of valve spring (2020)
  8. Kazaz, Lorin; Pfister, Christian; Ziegler, Pascal; Eberhard, Peter: Transient gear contact simulations using a floating frame of reference approach and higher-order ansatz functions (2020)
  9. Kulikov, G. Yu.: Nested implicit Runge-Kutta pairs of Gauss and lobatto types with local and global error controls for stiff ordinary differential equations (2020)
  10. Kulikov, G. Yu.; Weiner, R.: Variable-stepsize doubly quasi-consistent singly diagonally implicit two-step peer pairs for solving stiff ordinary differential equations (2020)
  11. Link, Kathryn G.; Sorrells, Matthew G.; Danes, Nicholas A.; Neeves, Keith B.; Leiderman, Karin; Fogelson, Aaron L.: A mathematical model of platelet aggregation in an extravascular injury under flow (2020)
  12. Montagu, E. L.; Norbury, John: Unusual bifurcation of a Neumann boundary value problem (2020)
  13. Oliveira, Karen A.; Berbert, Juliana M.: Crossover in spreading behavior due to memory in population dynamics (2020)
  14. Skvortsov, L. M.: Construction and analysis of explicit adaptive one-step methods for solving stiff problems (2020)
  15. Störkle, Johannes; Eberhard, Peter: Model-based vibration control for optical lenses (2020)
  16. 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)
  17. Towne, Aaron; Lozano-Durán, Adrián; Yang, Xiang: Resolvent-based estimation of space-time flow statistics (2020)
  18. Abdi, A.; Jackiewicz, Z.: Towards a code for nonstiff differential systems based on general linear methods with inherent Runge-Kutta stability (2019)
  19. Belov, A. A.; Kalitkin, N. N.: Efficient numerical integration methods for the Cauchy problem for stiff systems of ordinary differential equations (2019)
  20. 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)

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