Hi, is there some method for eliminating dual solutions to a given differential equation that are not wanted? Let me explain: Consider the differential equation
where is a linear operator (that doesn't operate in the time dimension). However, since the equation is going to be solved numerically, and the operator is very computationally expensive to be implemented directly, the equation is modified:
where is much computationally cheaper to implement. However, this equation gives dual solutions that do not satisfy the original equation (*), since (**) can be shown to allow any linear combination of solutions to the equations
(*, our original equation)
So the modified equation can't be used solely. Is there some way to eliminate the solutions given by (***) when solving the system numerically, and only obtain solutions given by (*)? Thanks in advance.