I am looking to implement the 1D Klein-Gordon equation $u{tt} - u{xx} + V = 0$ using the py-pde package but I am having some issues, specifically as the evolution operator is a second order derivative in time. I have looked at the tutorials and examples but they all seem to have an LHS as a first order derivative in time. Is there a method to do this in py-pde?
Thanks
Yes, the package only supports first-order derivatives in time, but you can easily introduce an auxiliary field, $f=\partial_t c$, to turn your equations into a coupled system with first-order time derivatives.
Hi there,
I am looking to implement the 1D Klein-Gordon equation $u{tt} - u{xx} + V = 0$ using the py-pde package but I am having some issues, specifically as the evolution operator is a second order derivative in time. I have looked at the tutorials and examples but they all seem to have an LHS as a first order derivative in time. Is there a method to do this in py-pde? Thanks