# How to solve a highly nonlinear PDE

GROUPS:
 I have a highly nonlinear PDE, in a formD[f[x,y],x]^2==Gwhere f[x,y] is the function I wanna solve. G is some function of f[x,y], D[f[x,y],x], x and y.So,there are two solutions:D[f[x,y],x]=-Sqrt[G],and D[f[x,y],x]=+Sqrt[G]after specify some initial conditions, I can first solve the first one (- sign), numerically. then at some point, this solution terminates because of singularies or something else (the solution, which is a interpolating function, will turn from a real value to a complex value). The terminating point is a line y0=y0. At this point I want to change the equation to the (+ sign) one, with the new initial conditions given by f[x,y0[x]].How can I do the above steps?Especially, first, how can I get this terminating line y0=y0; second, how can I specify f[x,y0] as the new initial conditions?By the way, how to make Mathematica solve PDE only in real number field?
4 years ago
4 Replies
 Because there is in general no closed form solution for non-linear PDE/ODE, you want to be very specific about the actual function that you are dealing with. A good idea is to give a set of real values for demonstration.