- #1
SeM
Hello, I haven't found any program that can be used to perform separation of variables on difficult PDEs. Is there such a method somewhere?
This is the one I wanted to simplify further, but I suspect it is not possible:NFuller said:Programs can numerically solve PDEs. Separation of variables is a trick that you can use to solve some types of PDEs on paper.
Not all PDEs are separable, if you can't do it then a program can't do it either. Where does this PDE come from? There may already be special methods for solving it.SeM said:I have already done separation of variables, and can't get rid of the 1/RY term.
What database? There are various methods for dealing with certain classes of PDEs, boundary layer rescaling comes to my mind, but no method works for everything.SeM said:Hi, I wish it was so easy. If you see on literature database, there are several emerging methods for simplifying very complex PDEs using matrix reps, linear algebra and other approaches
scholar.google.comNFuller said:Not all PDEs are separable, if you can't do it then a program can't do it either. Where does this PDE come from? There may already be special methods for solving it.
What database? There are various methods for dealing with certain classes of PDEs, boundary layer rescaling comes to my mind, but no method works for everything.
How do you know this is zero? This implies that either ##r## is zero or the denominator goes to infinity.SeM said:The strange term r^2/RY = 0
It would help to see the original PDE before you attempt separation of variables. The fact that you are having trouble likely means that separation of variables will not work here i.e. the solution cannot be written as the product of two functions with only ##r## and ##\theta## dependence.SeM said:Is this OK as a method?
Separation of variables is a method used in MATLAB to solve differential equations by breaking them down into simpler equations that can be solved individually.
In MATLAB, separation of variables works by assuming that the solution to the differential equation can be expressed as a product of two functions, each of which only depends on one of the variables in the equation.
Separation of variables is most useful for solving linear differential equations with constant coefficients. It can also be used for nonlinear equations, but the process can be more complex.
The general process for using separation of variables in MATLAB involves first rearranging the differential equation into a form where the variables are separated on opposite sides. Then, each side is set equal to a constant, and these constants are used to solve for the individual functions. The final solution is then obtained by combining the two functions with their corresponding constants.
Yes, there are limitations to using separation of variables in MATLAB. This method can only be used for linear differential equations with constant coefficients, and it may not always produce an exact solution. It also requires that the equation can be rearranged into a form where the variables are separated on opposite sides.