## 60 Reputation

4 years, 108 days

## Solving a nonlinear hyperbolic PDE...

Maple 2015

I am considering the following PDE and I am getting an error, please suggest a better numerical method than the default one used in maple:

the PDE is:

u_{xx}u^3 - sin(xt)u_{tt} = u(x,t)

u(x, 0) = sin(x), (D[2](u))(x, 0) = cos(x), u(0, t) = cos(t), (D[1](u))(0, t) = sin(t)

Please suggest me a method that will also work for the following PDEs:

u^m* u_{xx} - sin(xt)u_{tt} = u^n

for m,n =0,1,2,3,... for the cases m=n and m not equal n

Here's the code:

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## Wave PDE equation...

Maple

I have the following PDE:

u_xx = u_tt + (2^{1/2}u_x-u)^{1/2}

Do you have a proposed algorithm to solve in maple for this PDE? I mean pdsolve won't solve it because it's a nonlinear PDE.

## PDE to solve numerically...

Maple 2015

I want to solve numerically the PDE:

u_xx + u_yy= = u^{1/2}+(u_x)^2/(u)^{3/2}

My assumptions are that  |sqrt(2)u_x/u|<<1 (but I cannot neglect the first term since its in my first order approximation of another PDE.

So I tried solving by using pdsolve in maple, but to no cigar.

Here's the maple file:

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## Another PDE to solve numerically....

Maple 2015

I want to solve numerically the nonlinear pde:

u_x+u_t - (u_{xt})^2 = u(x,t)

which method do you propose me to use with maple? (I don't mine about which boundary conditions to be used here).

## Checking a theorem about ultrahyperboli...

Maple

I have the following paper:

Now I wanted to check Fritz John's claim in the proof of Theorem 1.1, he says that equation (7) can be easily verified for case i=1,k=2.

Now at first I tried to calculate by hand, but it's just a lengthy calculation, so now I turned to maple to check its validity, I get that this claim is false, am I wrong in my code? if yes, then how to change it?

P.S

I changed between xi and x and eta and y.

In the following is the code:

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