Hey!
I am kind of new to mathematica so I don't know a lot of stuff...
So trying to put the question in context... I want to know if there is a way in Mathematica 9 to solve
Nonlinear Second Order Parial Differential Equation?
I understand that I cannot use
DSolve since its a Second Order PDE but even with
NDSolve, I keep getting errors..
My
PDEs are something like this:
fpde = (1 + (D[y[x, t], t])^2) (D[y[x, t], {x, 2}]) + (1 + (D[y[x, t], x])^2) (D[y[x, t], {t, 2}]) == 0;
i.e.
(1 + (
dy /
dt)^2 ) * (
d2y /
dx2)) + (1 + (
dy /
dx)^2 ) * (
d2y /
d?t2)) = 0
where y is a function of x and t.
I also give
two boundary conditions and
one initial conditon while using NDSolve
I have tried the following:
mysol = NDSolve[{fpde, y[0, t] == 0, y[2 Pi, t] == 0, y[x, Pi/4] == 0}, y, {x, 0, 2 Pi}, {t, 0, 2 Pi}]
Error : The number of constraints (1) (initial conditions) is not equal to the total differential order of the system plus the number of discrete variables (2).
mysol = NDSolve[{fpde, y[0, t] == 0, y[2 Pi, t] == 0, Derivative[1, 0][y][x, 2 Pi] == Tan[x]}, y, {x, 0, 2 Pi}, {t, 0, 2 Pi}]
Error: Boundary values may only be specified for one independent variable. Initial values may only be specified at one value of the other independent variable.
I can't figure out if my application of the command is incorrect or if a different approach is required to solve such PDEs.
My objective is to get the numerical solution to such an equation.Thanks a lot!
