5 years, 29 days

## 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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## Recursive integral equation...

Maple 18

I want to find numerically the limit lim(y[m](t),m = infinity), do you have an idea how to do implement it in maple?

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## An integral equation to solve ...

I have the following integral equation to solve numerically:

v(x,t)=1 - h*\int_0^t JacobiTheta0(1/2x , \pi i s) v^4(1,t-s)ds

where h is a numerical parameter, and v(1,t) = 1-h*\int_0^t \theta_3(r)v^4(1,t-r)dr (theta3 is Jacobi theta3 function).

So I want to use an iteration method that will converge numerically to the solution, where v(1,0)=1.

How to use maple for this?

I want also to find the rate of convergence to the numerical solution.

edit: I should note that v(x,0)=1, even though it's implied from v(x,t) above.

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