2.3 Simulation Center
37
In addition, you should set the number (number of intervals) or the length of the
intervals (interval length) to display graphical results, although the listed parameters
can also be taken as specified in WSM by default.
2.3.2 Solver Selection
In most cases, the mathematical model of dynamic systems is determined by differential (ordinary) and algebraic equations. There is an extensive literature on the
theory and methods for solving these equations [5–22].
To solve systems of algebraic and differential equations specifically in the Wolfram SystemModeler environment (version 4.2) [1], the following methods are used
(solver field, Fig. 2.12):
• DASSL;
• CVODES;
• explicit Euler method (with fixed step);
• Heun’s method (with fixed step);
• fourth-order Runge–Kutta method (with a fixed step).
In this case, all numerical methods in this version of Wolfram SystemModeler allow solving only ordinary differential equations of the first order. In this
regard, ordinary differential equations that determine the mathematical model of the
dynamical system under consideration should be reduced to first-order differential
equations.
In the settings of the computational experiment, it is possible to independently choose the method by which the determining equations are included in the
mathematical model, as shown in Fig. 2.12.
The DASSL and CVODES methods themselves control the integration step,
whereas for the rest of the methods the integration step is fixed and can be set
by the user (the step size field).
Since the number of integration steps is usually large, not all steps can be displayed
on charts, but only a certain number of them (the number of intervals field). Or,
alternatively, you can specify the step length (the interval length field) with which
points will be drawn on the graphs. Such settings can be useful, for example, if the
function oscillates quickly and its graph does not look smooth enough.
DASSL
Differential/Algebraic System Solver (DASSL) [19] is designed for the numerical
solution of implicit systems of differential or differential–algebraic equations for
y ∈ R
N with given initial conditions:
F(t, y, y
) = 0, y(t 0 ) = y 0 .
37
In addition, you should set the number (number of intervals) or the length of the
intervals (interval length) to display graphical results, although the listed parameters
can also be taken as specified in WSM by default.
2.3.2 Solver Selection
In most cases, the mathematical model of dynamic systems is determined by differential (ordinary) and algebraic equations. There is an extensive literature on the
theory and methods for solving these equations [5–22].
To solve systems of algebraic and differential equations specifically in the Wolfram SystemModeler environment (version 4.2) [1], the following methods are used
(solver field, Fig. 2.12):
• DASSL;
• CVODES;
• explicit Euler method (with fixed step);
• Heun’s method (with fixed step);
• fourth-order Runge–Kutta method (with a fixed step).
In this case, all numerical methods in this version of Wolfram SystemModeler allow solving only ordinary differential equations of the first order. In this
regard, ordinary differential equations that determine the mathematical model of the
dynamical system under consideration should be reduced to first-order differential
equations.
In the settings of the computational experiment, it is possible to independently choose the method by which the determining equations are included in the
mathematical model, as shown in Fig. 2.12.
The DASSL and CVODES methods themselves control the integration step,
whereas for the rest of the methods the integration step is fixed and can be set
by the user (the step size field).
Since the number of integration steps is usually large, not all steps can be displayed
on charts, but only a certain number of them (the number of intervals field). Or,
alternatively, you can specify the step length (the interval length field) with which
points will be drawn on the graphs. Such settings can be useful, for example, if the
function oscillates quickly and its graph does not look smooth enough.
DASSL
Differential/Algebraic System Solver (DASSL) [19] is designed for the numerical
solution of implicit systems of differential or differential–algebraic equations for
y ∈ R
N with given initial conditions:
F(t, y, y
) = 0, y(t 0 ) = y 0 .