Linked Questions

3
votes
1answer
293 views

PDE with NDSolve gives solution despite not enough boundary conditions [duplicate]

For a given PDE, uniqueness of the solution requires boundary/initial conditions, the exact type of conditions depending on the particular PDE under consideration. For example consider the wave ...
17
votes
3answers
1k views

Numerically solve the initial value problem for the 1-D wave equation

I want to solve the standard 1-dimensional wave equation $y_{xx}=y_{tt}$ using NDSolve (for $y(x,t)$) with the following conditions: ...
9
votes
1answer
417 views

PDEs : automatic method choice : TensorProductGrid or FiniteElement?

A problem that arises when we solve PDEs with NDSolve[] and Method->Automatic is how to know which method has been chosen : <...
2
votes
3answers
316 views

How to take derivative of the argument of an interpolating function

I am trying to plot the derivative of the argument of an interpolating function u[t, x] with respect to $x$. Here, u[t, x] is ...
3
votes
1answer
450 views

How to modify a PDE inside NDSolve according to an if condition

I need to solve this PDE $$\partial_tf(t,x)+\partial_xf(t,x)+k\partial_{xx}f(t,x)-xf(t,x)=0 $$ with $k\in\mathbb{R}$ and final condition $f(T,x)=1$ with $0<t<T$. My problem is how to solve ...
2
votes
2answers
682 views

Solving systems of partial differential equations with functions of different number of variables

I am trying to solve the following system of two partial differential equations $\partial_t G(x,y,t) + \partial_x G(x,y,t)+\partial_y G(x,y,t) = -i\left[f(x,t) + f(y,t)\right] $ $\partial_t f(x,t) + ...
6
votes
1answer
244 views

Solving a system of coupled non-linear partial differential equations

I am trying to solve a system of coupled non-linear partial differential equations, 2D spatially + time. The equations are: where c, d, and p are constants. I am solving for the functions Az and Bz ...
1
vote
2answers
185 views

A numerical boundary conditions paradox

For $(t,z)\in[0,1]\times[-1,0]$ zmin = -1; tmax = 1; and some fields $w(t,z)$ and $y(t,z)$ ...
0
votes
0answers
499 views

Solution of Fokker-Planck equation with delta initiall condition - everywhere zero

I try to solve a Fokker-Planck equation (which I derived from corresponding Ito equation) $\partial_tp=-\sum\limits_{i=1}^4 \partial_{x_i}(\mu_i p)+\frac{1}{2}\sum\limits_{i=1}^4 \sum\limits_{j=1}^4\...
1
vote
1answer
151 views

NDSolve: method of lines: unexpected error: insufficient boundary conditions

As a test of my ability to master the Method of Lines I tried to NDSolve the PDE's system $$\partial_t \varphi = \varpi\qquad\partial_t\varpi=\frac{1}{r}\partial^...
2
votes
1answer
163 views

Singularity while solving PDE

I have to solve a PDE (in the context of the functional renormalization group in physics). I have a function of two variables, $U(l,p)$. I know $U(0,p)=U_0(p)$ and then I have an equation (eq925) that ...
2
votes
1answer
269 views

Automatic Boundary conditions in NDSolve

I would like to know what kind of boundary conditions Mathematica implements in NDSolve when not specifying any boundary conditions by hand. So for example solving ...
1
vote
0answers
209 views

Solve nonlinear coupled PDE with x,y and t dependent

I am trying solve the following two coupled PDE equations. ∂f/∂t=(∂^2 f)/(∂x^2 )+(∂^2 f)/(∂y^2 )-1/f^3 [(∂B/∂x)^2+(∂B/∂y)^2 ]-f+f^3 (∂^2 B)/(∂x^2 )+(∂^2 B)/(∂y^2 )-B*f^2+2/f [(∂B/∂x)(∂f/∂x)-(∂B/∂y)(...
1
vote
0answers
161 views

Solving the non-linear heat equation numerically

I need to solve the following equation $\frac{\partial^2 \Phi}{\partial u^2}=\frac{\partial \Phi}{\partial u} \frac{\partial \Phi}{\partial \tau}$ with some initial condition $\Phi (u,0)$ to which the ...
1
vote
0answers
134 views

Solving Burger's equation and continuity with a pressure forcing term for a gas [closed]

I'm trying to solve this Burger's equation and continuity with a pressure forcing term. Below is the code snippet that I've tried already for the non-dimensionalized equations. The parameter ...

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