Modelica.Math.Nonlinear.Examples

Information

Package Content

Name	Description
quadratureLobatto1	Integrate integral with fixed inputs
quadratureLobatto2	Integrate integral with user dependent inputs
solveNonlinearEquations1	Solve nonlinear equations with fixed inputs
solveNonlinearEquations2	Solve nonlinear equations with user dependent inputs
quadratureLobatto3	Integrate function in a model
UtilityFunctions	Utility functions that are used as function arguments to the examples

Modelica.Math.Nonlinear.Examples.quadratureLobatto1

Information

This example integrates the following integrands with function quadratureLobatto and compares the result with an analytical solution. The examples also demonstrate how additional input arguments to the integrand function can be passed as additional arguments. The following integrals are computed:

• integral(sin(x)*dx) from x=0 to x=1
• integral(sin(5*x)*dx) from x=0 to x=13
• elliptic integral from x=0 to pi/2

Inputs

Name	Description
tolerance	Error tolerance of integral values

Modelica.Math.Nonlinear.Examples.quadratureLobatto2

Information

This example solves the following integrands with function quadratureLobatto. The user can set the parameters, like "w" or "k", and can experiment with different integration intervals. The following integrals are computed:

• integral(sin(x)*dx)
• integral(sin(w*x)*dx)
• elliptic integral

Inputs

Name	Description
General
Tolerance	Error tolerance of integral value
Sine
a1	Lower limit
b1	Upper limit
Sine w
a2	Lower limit
b2	Upper limit
w	Angular velocity
Elliptic integral
a3	Lower limit
b3	Upper limit
k	Modul

Modelica.Math.Nonlinear.Examples.solveNonlinearEquations1

Information

This example solves the following nonlinear equations with function solveOneNonlinearEquation and compares the result with the available analytical solution. The examples also demonstrate how additional input arguments to the nonlinear equation function can be passes as additional arguments. The following nonlinear equations are solved:

• 0 = u^2 - 1
• 0 = 3*u - sin(3*u) - 1
• 0 = 5 + log(u) - u

Inputs

Name	Description
tolerance	Relative tolerance of solution u

Modelica.Math.Nonlinear.Examples.solveNonlinearEquations2

Information

This example solves the following nonlinear equations with function solveOneNonlinearEquation. The user can set the parameters, like "w" or "m", and can experiment with different start intervals. The following nonlinear equations are solved:

• 0 = u^2 - 1
• 0 = 3*u - sin(w*u) - 1
• 0 = p[1] + log(p[2]*u) - m*u

Inputs

Name	Description
General
tolerance	Relative tolerance of solution u
u^2-1
u_min1	Lower limit
u_max1	Upper limit
3*u - sin(w*u) - 1
u_min2	Lower limit
u_max2	Upper limit
w	Angular velocity
p[1] + log(p[2]*u) - m*u
u_min3	Lower limit
u_max3	Upper limit
p[2]	Parameter vector
m	Parameter

Modelica.Math.Nonlinear.Examples.quadratureLobatto3

Information

This example demonstrates how to utilize a function as input argument to a function in a model.

Parameters

Name	Description
A	Amplitude of integrand of s
ws	Angular frequency of integrand of s
wq	Angular frequency of q