Polar

{  POLAR.PDE  }

{

  Test equations in polar form, using function definitions to expand polar

  derivatives in cartesian (XY) geometry.

}

title 'Polar Coordinates'

Variables

    u

definitions

    k = 1

    u0 = 1-r**2

    s = 4

    dr(f) = (x/r)*dx(f) + (y/r)*dy(f)                { functional definition of polar derivatives... }

    dphi(f) = (-y)*dx(f) + x*dy(f)                {... in cartesian coordinates }

equations        { Multiply by r^2 to clear the singularity }

   r*dr(r*dr(u)) + dphi(dphi(u)) + r*r*s = 0

boundaries

    Region 1

       start(0,0)

       natural(u) = 0 line to (1,0)

       value(u)=u0 arc(center=0,0) angle=90

       natural(u)=0 line to close

monitors

    grid(x,y)

    contour(u)

    contour(u-u0)

plots

    grid(x,y)

    contour(u)

    contour(u-u0)

end