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

learn more… | top users | synonyms (3)

1
vote
0answers
54 views

Getting FindRoot::nlnum when trying to find root of an Interpolating function

I want to solve a system of differential equations and find a point where the solutions cross. So four steps: 1. Solve the system of differential equations: ...
-3
votes
0answers
52 views

Mathematica Bug with version 10.4.10 with OSX [on hold]

I have upgraded mathematica to 10.4.10 and OSX El Capitan version 10.11.4. On my desktop I use linux and mathematica version 9. I have a notebook on the desktop that run just fine ( I am solving ...
2
votes
0answers
33 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
0answers
94 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?
1
vote
1answer
33 views

NDSolve for complex variables

I am trying to simulate a multiple pendulum system with damping as follows: ...
12
votes
1answer
410 views

Mathematica9: NDSolve slows down after repeated calls

Bug introduced in 9.0 or earlier and persisting through 10.4.1 or later I have noted that in Mathematica 9 my code, which involves a lot of calls to NDSolve, ...
5
votes
1answer
147 views

Systematic increase in runtime [duplicate]

When I run this simple code, which repeats many times the exact same operation (a differential equation), the runtime (given by Timing) increases systematically, ...
9
votes
1answer
113 views

Memory leak with NDSolve

This is not the first time the question in mentionned (cf in particular this recent question NDsolve memory leak), but there seems to be a serious issue of memory leak - or am I missing something? ...
4
votes
1answer
77 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&...
6
votes
1answer
176 views
+50

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 ...
0
votes
0answers
31 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 ...
0
votes
2answers
78 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] ...
4
votes
1answer
46 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 ...
16
votes
1answer
1k views

I failed to solve a set of one-dimension fluid mechanics PDEs with NDSolve

The fluid here has been assumed as single component perfect gas i.e. it obeys the equation $p=ρ R T$, the thermal conductivity is assumed as a constant, so the equation set is: ...
0
votes
2answers
80 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 ...
4
votes
2answers
129 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) ...
4
votes
1answer
118 views

Solving 2D Laplace equation for irregular boundaries [on hold]

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
1answer
109 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
1answer
60 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
2
votes
2answers
64 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 ...
0
votes
0answers
49 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 ...
0
votes
0answers
49 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) ...
1
vote
1answer
60 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): ...
1
vote
1answer
103 views
8
votes
1answer
510 views

NDSolve and memory usage

After some googling, i've found similar problems around, but didn't find a 100% satisfactory answer, so let me ask here: I'd like to solve a 1+1 problem using the method of lines. In spherical ...
1
vote
1answer
67 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: ...
3
votes
1answer
50 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
4answers
747 views

Implementing Picard's Iteration for solving ODEs

Picard's Iteration is a way of solving the IVP $$y'(x)=f(x,y(x)), \quad y(x_0)=y_0 $$ It consists of defining the following sequence of functions recursively: $$y_0(x):=y_0 \\ y_{n}(x):=y_0+\int_{...
7
votes
1answer
83 views
0
votes
0answers
35 views

NDSolve is not giving any result nor any error [closed]

I am trying to solve a differential equation for $\psi$, but NDSolve is not giving any result nor any error. Please help me. My function is ...
7
votes
1answer
76 views

Issuing with ParametricNDSolveValue

I am having a problem with ParametricNDSolveValue[] . let me start with a simple example. Considered following example with constant parameter $a$. ...
0
votes
0answers
94 views

How can I solve this PDE? [on hold]

I have been trying to solve this PDE, but Mathematica didn't give me a solution. Here it is: ...
2
votes
1answer
55 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 ...
0
votes
0answers
93 views

Animating ballistic movement [on hold]

I was tasked with creating a 3D animation of the movement of a ball through space, while taking into account influences such as the magnus effect, air drag, and rotation. In order for this to happen a ...
13
votes
2answers
266 views

Heat convection differential equations from 1952 - Mathematica “fails to converge”

I am trying to solve a fundamental problem in analytical convective heat transfer: laminar free convection flow and heat transfer from a flat plate parallel to the direction of the generating body ...
0
votes
0answers
53 views

Saving the result of a NDSolve

I have solved this diff equation (with no problems): ...
2
votes
3answers
110 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? <...
1
vote
1answer
91 views

To deal with infinity in NDSolve

I just started to learn to use Mathematica, and was trying to obtain an inverse function. Helpful comments lead to the use of NDSolve, but I encountered the problem ...
0
votes
1answer
35 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: ...
0
votes
1answer
203 views

How to pass arguments in NIntegrate and NDSolve

I am solving PDEs with NDSolve and NIntegrate, but I do not know how to pass arguments correctly. My orignial code is very ...
0
votes
0answers
39 views

Singularity/Stiff system error

I am after the solutions of the coupled differential equations ...
0
votes
2answers
114 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: ...
-1
votes
1answer
128 views
0
votes
1answer
63 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
3answers
128 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 ...
6
votes
1answer
117 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
64 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(-...