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Behind and beyond the MATLAB ODE suite. (English) Zbl 0955.65055
Summary: The paper explains the concepts of order and absolute stability of numerical methods for solving systems of first-order ordinary differential equations (ODE) of the form \[ y'= f(t,y),\quad y(t_0)= y_0,\quad\text{where }f: \mathbb{R}\times \mathbb{R}^n\to \mathbb{R}^n, \] describes the phenomenon of problem stiffness, and reviews explicit Runge-Kutta methods, and explicit and implicit linear multistep methods. It surveys the five numerical methods contained in the MATLAB ODE suitable (three for nonstiff problems and two for stiff problems) to solve the above system, lists the available options, and uses the odedemo command to demonstrate the methods. One stiff ode code in MATLAB can solve more general equations of the form \(M(t)y'= f(t,y)\) provided the Mass option is on.

MSC:
65L20 Stability and convergence of numerical methods for ordinary differential equations
34-04 Software, source code, etc. for problems pertaining to ordinary differential equations
65L05 Numerical methods for initial value problems involving ordinary differential equations
65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems
68W30 Symbolic computation and algebraic computation
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