« View all new features in Mathematica 9  previous  |  next 
New in Mathematica 9Advanced Hybrid and Differential Algebraic Equations

Compute Sliding Mode Solutions 

Find solutions to differential equations in 2D and 3D with discontinuities that are automatically computed using Filippov sliding mode.

Compute a solution in the plane where there is a discontinuity on the unit circle.

In[1]:=
Click for copyable input
X
Out[1]=

When the solution first reaches the circle, the vector field on both sides points towards the discontinuity, leading to sliding mode along the circle until the vector field on the outside no longer points inward.

In[2]:=
Click for copyable input
X
Out[2]=

Compute multiple solutions.

In[3]:=
Click for copyable input
X
Out[3]=

In higher dimensions, sliding mode is possible on more than one discontinuity surface at once. This happens for two discontinuity surfaces in 3D defined by the surface of a sphere and the plane , with the vector field given by .

In[4]:=
Click for copyable input
X

Make a plot by forming contour surfaces for the discontinuities and using ParametricPlot3D for the solution curve.

In[5]:=
Click for copyable input
X
In[6]:=
Click for copyable input
X
Out[6]=