Linked Questions
16 questions linked to/from Numerical solution of coupled ODEs with boundary conditions
54
votes
4
answers
8k
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Dynamic Euler–Bernoulli beam equation
I am trying to solve for the vibration of a Euler–Bernoulli beam. The equation is
$\frac{\partial ^2u(t,x)}{\partial t^2}+\frac{\partial ^4u(t,x)}{\partial x^4}=0$
For the boundary conditions I ...
- 16.8k
8
votes
4
answers
5k
views
Nonlinear differential equation: numerical solution
I have to find and plot a numerical solution for this second order differential equation:
u''[x] + (u'[x]/x) - (u[x]/(x^2)) + u[x] - u[x]^3 = 0
where $0\leq x &...
user32475
7
votes
3
answers
506
views
Trouble with differential equation
I tried to solve this differential equation:
$$\epsilon y''(x)+xy'(x)=-\epsilon \pi^2 \cos(\pi x)-\pi x\sin(\pi x)$$
with boundary conditions: $y(-1)=-2, \space y(1)=0$. If we take $\epsilon=0.1$, ...
- 857
9
votes
2
answers
11k
views
ndsz : step size is effectively zero; singularity or stiff system suspected
This is the first time I ask a question. I have seen many solutions to this error and tried but they are not working.
Here is the code.
...
- 91
4
votes
2
answers
662
views
Why does NDSolve blow up when given my ODE but bvp4c in Matlab does not?
I am numerically solving the following ODE initially using NDSolve in Mathematica(updated and corrected):
$-(-\frac{z'(r)}{r \sqrt{z'(r)^2+1}}-\frac{z''(r)}{\left(z'(r)^2+1\right)^{3/2}})=A_1(z(r)+H)...
- 41
9
votes
2
answers
432
views
Error when solving 't Hooft-Polyakov radial equations using NDSolve
I'm trying to solve 2 coupled nonlinear ODEs using NDSolve, but the solution fails when the parameter $\lambda$ increases. The equations are
$$r^2 a''(r)= a(r) [a(r)-1] [a(r)-2]- r^2 [1-a(r)] h(r)^2,$$...
- 125
2
votes
2
answers
771
views
Solving 2D+1 PDE with Pseudospectral in one direction with periodic boundary condition?
According to the documentation about the pseudospectral difference-order:
It says:
Following the discussion here:
I found the messy behavior is always on the artificial boundary in $\omega$-...
- 445
3
votes
2
answers
480
views
Nonlinear system of ODEs with boundary conditions
I'm trying solve this problem:
g'(r) = a(r)g(r)/r, (1/r)a'(r) = g(r)^2-1
which have the following boundary conditions: a(0)=n ...
- 133
4
votes
2
answers
492
views
While loop with infinitesimal steps is too time consuming
I have two ODEs with initial conditions. I want to solve the system such that $10^{-4}<z[x]<z_{0}$. The difficulty of problem is here that the initial conditions in not fixed but the boundary ...
- 75
4
votes
1
answer
521
views
Computing Separatrix of Second-Order Nonlinear Autonomous ODE
Numerically solving differential equations of the form
{x''[t] == f[x[t], x'[t]], x[0] == x0, x'[tm] == 0}
where tm is large, ...
- 62.1k
4
votes
1
answer
818
views
Boundary value problem for 2 coupled ODE's using NDSolve: "singularity or stiff system suspected"
I'm trying to solve a pair of coupled ODE's. I need to place four Dirichlet boundary conditions (at R = 0 and R = ∞ for each ...
- 43
4
votes
1
answer
258
views
System of 3 second order non linear differential equations
I wish to solve the following system of equations:
$\frac{d^2f}{dr^2}- \frac{1}{r} \frac{df}{dr} = 2 f(r)\phi(r)^2$
$\frac{d^2\phi}{dr^2} + \frac{1}{r}\frac{d\phi}{dr} = \frac{1}{r^2} f(r)^2\phi(r) + \...
- 73
1
vote
1
answer
650
views
Solution of Coupled Second Order ODEs with Boundary Conditions
D[Tu1[x], {x, 2}] qu - Tu1[x] (fu0 + I w p) == Tou[x] f1
D[T1[x], {x, 2}] q - T1[x] (f0 - b g0 + I w p)==
To[x] (f1 - b g1) - g1
For T1 , ...
- 67
2
votes
0
answers
288
views
Boundary value problem, multiple dimensional shooting, coupled eigenvalue problem
Following the one dimensional boundary value problem here, I would like to understand the easiest way to solve a BVP for a coupled system. In the 1D case, BVP can be converted to an initial value ...
- 393
0
votes
0
answers
168
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How can I make NDSolve in version 11 use the same methods as version 9?
Sorry for the lack of a minimal working example but the code I am concerned about is rather large and I have no idea what the problem is. All I know is that when I run the code in Mathematica versions ...
- 355