Questions on the symbolic (DSolve, DifferentialRoot) and numerical (NDSolve) solutions of differential equations in Mathematica.

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3
votes
1answer
109 views

failure of code with Helmholtz equation with point source

I am new to the finite elements package in Mathematica. I have a system of equations, one of which is a Helmholtz equation with a point source in the interior of a bounded domain. The following is the ...
1
vote
0answers
35 views

Changing variable in numerical solution

I solved numerically the differential equation: ...
4
votes
1answer
78 views

Can I use operators of the form $\frac{d^2}{dx^2}+i\frac{d}{dx}$ inside NDEigensystem?

I am currently trying to find the eigenfunctions of Hamiltonians of the form $\hat H=\frac12 \hat p^2 +a\hat p +f(\hat x)$, and I thought I would give NDEigensystem ...
1
vote
0answers
91 views

Different results from ode45 and NDSolve?

I am solving nonlinear ODE + integration groups using NDSolve of mma and ode45 of matlab. At last, I found that they give different results, even after I added RungeKutta method, interpolationorder, ...
4
votes
0answers
47 views

Naive question on ODE numerical solving and periodic initial conditions

I have a second-order nonlinear ODE for which I would like to find a numerical solution, with periodic initial (boundary) conditions. Can this be done directly with ...
1
vote
1answer
51 views

NDSolve for complex variables

I am trying to simulate a multiple pendulum system with damping as follows: ...
5
votes
1answer
89 views

DSolve apparently returns wrong symbolic result

Bug introduced in 9.0 and persisting through 10.4.1 I am trying to get Mathematica to calculate the correct solution $x(t)$ of the following ODE: $\dot x = a x(t)+ct^n$ for $a>0$, $n\ge 1$, $c&...
0
votes
0answers
39 views

Question on Poincare section example

I'm trying to make a Poincare section. On the Wolfram Documentation Center they give an example that includes the lines ...
10
votes
1answer
161 views

Memory leak with NDSolve

Edit The technical team confirms the memory leak in NDSolve and has forwarded an incident report to the developers. This is not the first time the question in ...
4
votes
1answer
59 views

How to speed up NIntegrate when using an interpolating function output from NDEigensystem?

I have been working with NDEigensystem in order to find the resonant frequencies of different shaped drums. I would also like the coefficients of the different eigenfunctions so that each of these ...
4
votes
2answers
146 views

NDSolveValue Quality Issue

I'm having trouble with the resolution of the NDSolveValue solution. For example this code from here gives the following on my machine (Windows, Version 10.4.1): (Zoomed in to show detail) ...
0
votes
1answer
67 views

Manipulating of non linear differentials equation

I want to manipulate non linear differential equations $\dot{x}= x + g\, xy\quad \dot{y}= 1-2x^2-g\, y^2$ where g as parameter.but I don't get any curve on display. Plz help me
0
votes
2answers
93 views

Plotting the solution of a Chini differential equation

In DIFFERENTIAL EQUATION SOLVING WITH DSOLVE by D. Kapadia, there is a Chini differential equation : sol = DSolve[x'[t] == 5 x[t]^4 + 3 x[t]^(-4/3), x[t], t] ...
0
votes
1answer
122 views

Solving Partial Differential Equations using NDSolve

I'm trying to solve the following partial differential equation: With the boundary conditions: I could use another way to resolve this, like the finite volume method, but after I solve the ...
0
votes
0answers
109 views
4
votes
1answer
137 views

Solving 2D Laplace equation for irregular boundaries [closed]

I want to solve Laplace equation in 2D with $x$ and $y$ coordinates with the boundary conditions $V(0,y)=-180$; $V(x,0)=50x-180$; $V(x,6)=50x-180$; $V(453.595-\sqrt{450.05^2 - (y - 3)^2},y)=0$ The ...
0
votes
0answers
52 views

Mathematica treating a system of 1st order nonlinear ODEs as a system of DAEs

I'm trying to use NDSolve to solve a system of 1st order nonlinear ODEs. The system of equations is way too long to post here, but it is in the canonical form: $x_i'(t)=f_i(t,x)$. My problem is that ...
1
vote
0answers
98 views

Differential algebra package in Mathematica

Is there any equivalent of Maple's differential algebra package in Mathematica? In particular, the Rosenfeld-Groebner algorithm has been implemented?
0
votes
2answers
93 views

NDSolve with CUDALink

I am solving a system of non linear differential equations. The time needed to solve them is quite long and I would like to shorten it. Is it possible to send the NDSolve command to be solved by the ...
2
votes
2answers
76 views

Slow evaluation of Recurrence plot data from NDSolve: Performance Tuning

I am trying to use a recurrence plot to pinpoint the location when a system re-visits a previous point in its phase portrait. The system (a thin liquid film) is governed by a non-linear differential ...
1
vote
1answer
62 views

ParametricPlot3D shows an empty box

I'm trying to visualize numerical solution of 4 differential equations (these are the coordinates of a wave function in a quantum mechanical system): ...
8
votes
2answers
271 views

Finite difference method not converging to correct steady state or conserving area?

I am working with the following PDE, which is an advection-diffusion type equation. It describes the movement of a fluid-fluid interface inside an annulus of inner radius $R_1$ and outer $R_2$ under ...
1
vote
1answer
103 views

Not getting the correct solution of a second order ODE [closed]

This is the original question My code is ...
0
votes
0answers
50 views

Help in controlling NDSolve

I have a system of PDE's with initial and boundary conditions I'm solving using NDSolve. There is one term in the system (v) ...
3
votes
1answer
52 views

Solving biharmonic equation with Mathematica

I would like to solve a biharmonic equation in polar coordinates of the form: $\Delta \Delta \Phi[r,\theta] = r^i cos(j \, \theta) \quad i,j \, \epsilon \, \mathbb{N}_0 $ I know that a solution for ...
7
votes
1answer
86 views

NDSolve how to monitor shooting method iteration?

here is a shooting method solution right out of the docs: ...
1
vote
1answer
71 views

Stiffness problem in an NDSolve system. StiffnessSwitching does not help?

I'm trying to solve an ODE system with the NDSolve method. This my ODE system, with the BC and the functions V and dV defined: ...
0
votes
0answers
58 views

Saving the result of a NDSolve

I have solved this diff equation (with no problems): ...
2
votes
1answer
56 views

Problem using Nintegrate and NDsolve

I am going to use Nintegrate to integrate the result of NDsolve and also a Table. How I can ...
7
votes
1answer
81 views

Issuing with ParametricNDSolveValue

I am having a problem with ParametricNDSolveValue[] . let me start with a simple example. Considered following example with constant parameter $a$. ...
2
votes
3answers
113 views

How to integrate numerically the product of result of NDsolve? [closed]

I am going to integrate the product of the results of NDsolve, in fact If x and y are the results as interpolating function, How I can integrate x*y numerically? <...
0
votes
1answer
37 views

NonlinearModelFit error: the function value is not a list of real numbers with dimensions {101} at {a,k,m0} = \ {1.,1.,1.} [closed]

So I'm trying to find a sigmoidal fit for my numerical solutions of these two ODEs but I keep getting an error and I don't know how to get around it. Here's my code: ...
1
vote
1answer
133 views

To deal with infinity in NDSolve

Edit: According to Michael E2's comments, I did a few trail and error, and modify the question so that it uses exactly the same expressions I am having difficulties....
0
votes
2answers
117 views

Solving a set of nonlinear equations

I am trying to setup and solve a set of nonlinear equations. I keep getting an error. Here is my problem: ...
6
votes
1answer
122 views

How to numerically solve a 1D time-independent Schrödinger equation for two interacting particles

Solving the 1D single-electron time-independent Schrödinger equation has been demonstrated using NDEigensystem here. There, the single-electron Schrödinger equation ...
0
votes
0answers
18 views

Simple heat equation with exponential reaction term [duplicate]

This is the heat equation that i want to solve $${\partial T\over\partial t}={{1\over r^2}{\partial\over \partial r}(r^2{\partial T\over \partial r})+qAC_0exp(-E_a/RT) } \ \ \ 0<t<10, \ \ \ 0<...
0
votes
0answers
67 views

Nonlinear coupled equation (heat equation with source term)

I modeled simple chemical reaction-diffusion equation in spherical region $0\le r\le L$ $${\partial T\over\partial t}={{1\over r^2}{\partial\over \partial r}(r^2{\partial T\over \partial r})+qACexp(-...
0
votes
0answers
59 views

Solving a complicated integro-differential equation

I'm trying to solve the integro-differential equation: $-(1+z) H(z) \frac{d f_{i}}{dz} = J_{i}(E',z) - f_{i} \sum_{j} n_{\nu_{j}} \sigma_{ij}(E',z) + \int_{E'}^{\infty}dE~\sum_{j,k}f_{k} n_{\nu_{j}} ...
0
votes
1answer
65 views

Error message when running NDSolveValue

I am trying to solve a set of differential equations but keep getting an error. See message below "NDSolveValue::ndnum: Encountered non-numerical value for a derivative at t=0" The system that I ...
2
votes
2answers
127 views

How to plot an Eddington-Finkelstein diagram

I need to plot the same thing as what is shown on the third picture of the site below (sorry, I'm unable to poste that picture here) : http://ion.uwinnipeg.ca/~vincent/4500.6-001/Cosmology/...
2
votes
3answers
130 views

NDSolve and differentiation of Abs

I have found several questions about the derivative of Abs and how it is not defined in the complex plane. What I have not found yet is a precise and simple ...
-2
votes
1answer
68 views

Neumann and Dirichlet eigenvalue problem - Eigenfunctions on the square [closed]

I don't know if I am in a good place to ask my question, but I'd like someone to create a visual support for a problem of mathematics. I was wondering what is the fundamental different between a ...
1
vote
2answers
87 views

Stop Integration in NDSolve

The following code executes properly for some choices of initial points and parameter c, but fails for other choices. Could the failure be due to computation outside of the defined t, x, and y ranges? ...
2
votes
2answers
262 views

Ion motion in uniform axial magnetic field and radial electric field [closed]

I'm trying to model an ion's 3D motion in a constant/uniform axial magnetic field and a radial electric field (similar to a cylindrical magnetron, but two positive parallel center electrodes offset by ...
0
votes
0answers
37 views

Evaluating solution from NDSolve at a specific point

sol = NDSolve[{eq, iv}, {f[x, t]}, {x, 0, 1}, {t, 0, 10}]; sol[0,1] I want to evaluate the solution from NDSolve at any given point, but when I do the above, ...
0
votes
1answer
47 views

Speeding up WhenEvent + NDSolve (Performance tuning and handling instabilities)

I am solving a non-linear partial differential equation using NDSolve. The equation models a liquid film on an isothermal solid substrate. As a result of various fluid physics mechanisms such as ...
8
votes
2answers
131 views

Bug in NDSolve/WhenEvent?

Bug introduced in v10. I'm fairly sure the following is a bug, and I would normally just report it to WRI. However, this is related to my answer to When using NDsolve, how to determine the ...
0
votes
2answers
59 views

DSolve non linear DE

probably my problem i´m gonna ask seems ridiculous and quite basic. I want to solve an equation with the following code, where a,b,c are parameters. But surprisingly they don´t appear in the solution. ...
0
votes
1answer
45 views

system of differential equations 3 DSolve [closed]

dS/dt = a - dS - λ S I + β R dI/dt = λ S I - (d + m)I dR/dt = m I- (d + β)R Solve the above equation and plot the curve.
3
votes
1answer
173 views

How can I combine NDSolve[] with NSolve[]

Consider the two below ODEs with following dependent B.C. In the boundary conditions $k$ is an unknown. $$y_1''(x)=x$$ $$y_2''(y)=0$$ $$y_1(1)=y_2(1)$$ $$y_1(-k)=y_2(-k)$$ $$\frac{\text{dy}_1(1)}{\...