The MATLAB ODE suite. (English) Zbl 0868.65040

Shampine, Lawrence F.; Reichelt, Mark W.

SIAM J. Sci. Comput. 18, No. 1, 1-22 (1997).

The paper presents mathematical and software developments that are the basis for a suite of programs for the solution of initial value problems \(y' = F(t,y)\), with initial conditions \(y(t_{0}) = y_{0}\). The solvers for stiff problems allow the more general form \(M(t)y' = f(t,y)\) with a nonsingular and sparse matrix \(M(t)\). The programs are developed for MATLAB, which influences the choice of methods and their implementation.

Reviewer: P.Y.Yalamov (Russe)

MSC:

65L05	Numerical methods for initial value problems involving ordinary differential equations
65L06	Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
34E13	Multiple scale methods for ordinary differential equations
34A34	Nonlinear ordinary differential equations and systems
34-04	Software, source code, etc. for problems pertaining to ordinary differential equations
65Y15	Packaged methods for numerical algorithms

Keywords:

software; initial value problems; MATLAB; stiff problems; Gear method; Rosenbrock method; nonstiff system; Runge-Kutta method; Adams method

Software:

ode113; ode23s; ode23; Matlab; ode45; Ode15s; MATLAB ODE suite