Questions on the symbolic (DSolve, DifferentialRoot) and numerical (NDSolve) solutions of differential equations in Mathematica.
0
votes
0answers
7 views
Solving eigenvalue BVP with an interface
I have a boundary-value problem, that is defined over two adjacent regions with an interface in the middle, that contains an eigenvalue $\lambda$. The boundary conditions and the equations are ...
0
votes
0answers
27 views
Solve equation of motion with Dirac-fermions?
I want solve a System with n equation of Motion in first order. In this equation of motion are creation and annihilation operators of Dirac-fermions. I cannot figure out how to describe the creation ...
0
votes
0answers
22 views
Solution of Laplace equation
Is it possible to solve
$\qquad Uxx + Uyy=0$
and
$\qquad U[0, y]=0, U[1,y]=0,U[x,0]=0,U[x<0.3,1]=10,U[x>0.7,1]=10$
and Neumann condition in (0.3, 0.7)?
2
votes
1answer
61 views
How can I obtain the domain of a resulting Interpolating Function?
I have a problem with obtaining the domain of resulting Interpolating Function in my calculations. I want to solve the following differential equation
...
1
vote
0answers
47 views
Analytical solve for biharmonic equation
I want to analytical Solve or numerical solve by Mathematica a biharmonic equation with homogeneous boundary conditions homogeneous?
I considered its solution using Fourier analysis, which is not ...
0
votes
0answers
53 views
Numerically evaluating functions with subscript or indices [on hold]
I am numerically solving a large set of coupled ODEs. The tutorial here:
http://reference.wolfram.com/language/tutorial/NDSolveIntroductoryTutorial.html
...is ...
0
votes
1answer
61 views
Struggling to use FindMinimum function
I am interested to solve two coupled 2nd order differential equations (see the link below). Given a working precision (wp), I would like to determine the initial condition (v0) for which the square of ...
3
votes
1answer
82 views
Mathematica has trouble solving this coupled differential equation
I'm trying to solve the coupled differential equations:
...
1
vote
0answers
91 views
Solve differential equation
I want to solve the next differential equation,
fun = t^2*x''[t] + 4/3*t*x'[t] - 2/3*(1 - (L^2)/(6*t^(2/3))) x[t] - (2*L^2)/(45*t^(2/3)) == 0
DSolve[fun, x, t]
...
0
votes
0answers
27 views
Arenstorf Orbits [on hold]
I am interested in restricted three body problem (Arenstorf Orbits). I am currently trying to reproduce the results described in the weblink mentioned below. However, I would like to know the ...
0
votes
0answers
71 views
using power series to numerically solve NS equations of a compressible viscous flow in cylindrical form [on hold]
Following this and this questions, I am trying to solve Navier–Stokes continuum equations in cylindrical form for a axisymmetric, compressible and vicious flow using power series. Consider the ...
5
votes
1answer
285 views
What does the syntax C[1][x][y] mean?
I am examining an integrability condition,
$$u_{3,122}=u_{3,123}.$$
Typing
DSolve[D[u3[x1,x2,x3],x1,x2,x2]==D[u3[x1,x2,x3],x1,x2,x3],u3,{x1,x2,x3}]
it into MMA ...
3
votes
2answers
110 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 ...
-1
votes
1answer
63 views
Several errors with InterpolatingFunction
I'm getting some error messages that don't make sense. Apologies, as the code is somewhat complex. Basically what I'm trying to do is solve a system of differential equations, then fill a table with ...
-1
votes
0answers
35 views
How to solve the following nonlinear differential equation? Numerical [closed]
where f(vt)=sin(v t); T_{1} (0)=1;T_{2}(0)=0;\Phi(m,k)=constant
1
vote
1answer
67 views
Coloring Points in a DensityPlot/ListDensityPlot
I have a PDE system, whose functions are $a=a(t, x, y)$, $b=b(t,x,y)$, and $c=c(t,x,y)$,
with Dirichlet null boundary conditions and initial conditions in the form of circle.
The respective code ...
2
votes
2answers
61 views
Problem using NonlinearModelFit to 2 coupled differential equations
I am trying to find the parameters of a set of differential equations given experimental data. Before I tackled my set of 12 equations, I tried to solve a simpler and similar 2 equation system but ...
1
vote
2answers
65 views
How to obtain the exact solution of a partial differential equation?
I know that Mathematica can solve a PDE numerically, but I wonder if it is possible to obtain the exact solution. For example, consider the heat equation
$$u_t = \kappa u_{xx} $$
Is it possible to ...
4
votes
1answer
134 views
Inviscid Burgers equation — multivalued wave
I'm quite new to Wolfram Mathematica. I need to create an animation of a Burgers Hopf equation's solution which becomes multivalued (somewhat of a breaking wave). Is it possible to do so in ...
0
votes
1answer
43 views
Problem solving BVP using NDsolve
I'm trying to solve an eigth-order linear ODE using NDsolve.
The Code I'm using is:
...
0
votes
0answers
41 views
NDSolve doesn't let me evaluate function at an arbitrary point [duplicate]
I have a piece of code that looks like this
sol = NDSolve[{x'[t] == - 2 x[t] + x[t]^2, x[0] == 1}, {x[t]}, {t, to, to + 0.01}];
And if I plot it it looks fine
<...
1
vote
1answer
172 views
Solving Integro-differential equation numerically with shooting method
This question is related a question I previously asked here
Solving integro-differential equation with boundary condition at infinity
and for which a solution was found . Now I am dealing with a ...
0
votes
0answers
50 views
Computer intensive system of ODEs
I have a really computer intensive system of ODEs to solve numerically, I have written the general form below:
Hi all, I have a difficult ODE system that I am unsure Mathematica can handle:
...
1
vote
1answer
43 views
Solving an ODE System with Multiple Initial Conditions
I am trying to use ParametricNDSolveValue to run ODE simulations with multiple initial conditions then plot the results with ...
7
votes
3answers
268 views
DFT for Helium atom
I'm trying to solve this problem
I'm not a Mathematica expert, but my program works perfect when
vhartree={0,0,..,0}
This is the program I wrote:
...
0
votes
0answers
47 views
Unstable Plotting a 3D Partial Differential Equation
I am currently trying to solve and plot the following differential equation,
$\frac{\partial f}{\partial t} = i \frac{\partial^{2} f}{\partial \eta \partial \xi} - \xi \frac{\partial f}{\partial \eta}...
1
vote
0answers
68 views
inequalitysolution [closed]
I have a function for which I would like to solve an inequality and find a range of r with respect to other quantities. I am not well familiar with Mathematica, ...
0
votes
1answer
85 views
No output for bifurcation diagram
I am plotting a bifurcation diagram for my system with A on x-axis following the code in, How to make a bifurcation diagram of the Lorenz system under a varying ...
3
votes
2answers
123 views
Increase Performance of WhenEvent in NDSolve
I'm trying to reset the value of functions $u_{i}$ when they reach a threshold $θ$. Below the threshold, they evolve according to a simple differential equation. The $r_{i}$ resets the derivative to ...
1
vote
0answers
75 views
2D heat conduction through an annulus with time-dependent boundary condition
So I had an old post a couple of days ago about a similar problem with Dirichlet boundary conditions for the inner and outer boundary. The link to the original post:
2D heat conduction/advection ...
2
votes
4answers
117 views
Plot with different colors the results of an NDSolve with vector solution
Consider the following toy example:
...
1
vote
2answers
115 views
Plotting an approximated Dirac Comb
I am trying to approximate a Dirac Comb to use in an NDSolve calculation but when I Plot it over a large interval, it misses ...
0
votes
0answers
54 views
DSolve gets stuck on system of differential equations with unassigned variable
Hopefully someone can help me with this problem. I'm running a fairly simple script that involves some matrix operations and ends with a fairly nasty system of differential equations:
...
0
votes
1answer
79 views
How to test if a solution of NDSolve is positive
I want to solve a differential equation numerically and determine one of the parameters in the D.E. The goal is to determine $M$ such that the function goes asymptotically to zero or to put it in a ...
1
vote
1answer
51 views
Solving two coupled first order differential equations
I have the following system of coupled differential equations:
$\frac{d x(t)}{dt} = c_1 x(t) - c_2 y(t) + \gamma_1(t)$ and $\frac{d y(t)}{dt} = c_2 x(t) - c_1 y(t) + \gamma_2(t)$
...
0
votes
1answer
82 views
2D heat conduction/advection through an annulus with Dirichlet Conditions
I want to simulate heat conduction (and advection) through an annulus and its surrounding material in 2D, as illustrated in this mesh:
For the heat conduction, I want two Dirichlet boundary ...
0
votes
0answers
127 views
Solving PDEs using Taylor series
I'm thinking of solving a Partial differential algebraic equation using multidimensional polynomial (i.e. Taylor series). Consider the PDAE:
$$\mathbf F \left( \mathbf x, \mathbf y, \frac{\partial ...
0
votes
1answer
86 views
Problem in plotting results of NDsolve
This is an ODE, I want to plot P on x-axis and vars on y-axis. My code works fine but gives an empty plot
...
0
votes
1answer
47 views
1
vote
1answer
44 views
NDSolve for Coupled Second Order PDEs
I have the following set of equations that I have reduced down from a larger third-order partial differential equation
$f(x,y,t) = p(x,y,t) - (x-y)\left(\frac{\partial}{\partial x} - \frac{\partial}{\...
1
vote
1answer
60 views
NDsolve and Coupled first order ODE solving [closed]
I am new to this community and also to Mathematica. I am trying to solve a set of coupled first order differential equations related to the shape of a liquid drop. The code is as follows :
...
0
votes
0answers
41 views
error using NDSolve
The code is not running. However instead of i^2 in the second term if I use i then it is working. But with i^2 fails.
...
3
votes
0answers
87 views
Postprocessing of FEM: extremely slow speed of NIntegrate
I've gone through the documentation for NDSolve FEM. There are quite a lot tips and techniques for accelerating NDSolve, and only quite few tips for post processing. Somehow I found out that the ...
1
vote
1answer
88 views
Solve PDE system with mixed parabolic–elliptic equations
I want to solve a mixed PDE Parabolic-Elliptic system,
subject to initial conditions u(x,y,0)=1 and v(x,y,0)=2-0.5 cos[(Pi x)/5].
The respective code version ...
2
votes
1answer
48 views
Large residual error when solving a 2D BVP with NDSolve and Finite Element Method
I'm trying to solve a simple PDE (an inhomogeneous Helmholtz equation) in a disk domain with center at $(1,0)$ and radius 0.5 using the following commands
...
0
votes
1answer
47 views
Solve an ODE involving an Interpolating function with Mathematica
Using Mathematica, I want to solve an ODE of an Interpolating Function. First I solve the ODE obtaining the function y[s] (or Y[s])
...
2
votes
0answers
83 views
How to Solve this Fokker-Planck Equation?
I need to solve this Fokker-Planck equation in Mathematica and my attempt to perform this integration is above:
My first attempt is above:
...
0
votes
1answer
83 views
2nd Order ODE with Optimal Control
I'm trying to solve an ODE where there is an optimal control problem involving a tradeoff between the flow cost c and the drift rate ...
0
votes
1answer
28 views
6
votes
1answer
178 views
The rectangular region composed of two triangular regions contains a pde connecting the bc of the first and the second kind
I'm going to solve the Laplacian equation of the electrostatic field, which consists of two triangular regions, a rectangular region, a square, and on the intersection of the two regions of $$y=x$$, ...
