Wrong modified equation in some cases

[James Sutherland]

Synopsis

For some discretizations, the modified equation that is generated is wrong.

Instructions to duplicate:

Here is some code that will show the problem:

from sympy import symbols,latex
from src.pymodpde import DifferentialEquation, i, n # import the differential equation and the indicies we need to use

u= symbols('u')
D= symbols('D')

pde = DifferentialEquation( dependentVarName='y',
                            independentVarsNames=['x'])

t = n+1
advection = ( pde.y(time=t,x=i) - pde.y(time=t,x=i-1) ) / pde.dx
diffusion = ( 
    pde.y(time=t,x=i-1) 
    - 2*pde.y(time=t,x=i)
    + pde.y(time=t,x=i+1)
) / pde.dx**2

pde.set_rhs( -u*advection + D*diffusion )

pde.generate_amp_factor()
# pde.display_amp_factor()
pde.generate_modified_equation(nterms=3)
pde.display_modified_equation()

Workaround

Changing

pde.display_modified_equation()

to

pde.symbolic_modified_equation()

results in a correct (I think) modified equation.

[Mokbel Karam]

I have addressed this issue in this commit 5e9631a