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

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4
votes
1answer
100 views

Issues with modeling pulses in a very simple system of DAEs

Bug introduced in 10.4.1 or earlier Bug has been confirmed by WRI [Case:3594387]: It does appear that the NDSolve function is not behaving properly in this case and an incident report has been ...
1
vote
1answer
53 views

Using NIntegrate inside NDSolve

I need to use NIntegrate inside NDSolve, for example: ...
0
votes
1answer
59 views

NDSolve error: Step Size is effectively zero; singularity or stiff system is suspected

my current project is numerically solve the Friedmann equation: (a-dot / a)^2 = H_0^2 (sigma_r / a^4 + sigma_m / a^3 + sigma_lambda + simga_k / a^2) What I did was split my equation into two ...
0
votes
1answer
51 views

Solving boundary-value problems within a specified region

Is it possible to use DSolve with non-initial boundary conditions? For example, eqn = a == b x'[z] + c x[z] over the region 0 to L, something like ...
3
votes
1answer
341 views

Problems with NDSolve and partial differential equations of several variables

Suppose we have the following partial differential equation: $$ 0 = \frac{ \partial w }{ \partial \tau } + \left( w + \sqrt{ h + \beta } \right) \frac{ \partial h }{ \partial \chi } $$ where $w$ = $w(\...
2
votes
1answer
333 views

NDSolve for axisymmetric problem

I would like to solve an axisymmetric Poisson equation on a disk with FEM. The code for Cartesian coordinates works fine: ...
2
votes
0answers
84 views

Solving Differential Equation for derivative

I am new to mathematica and am trying to solve a differential equation. Actually, I am not entirely sure if the system can be called differential equation. I am interested in finding out the second ...
1
vote
1answer
104 views

Euler-Bernoulli cantilever beam with parabolic load

How do I obtain the displacement in the free end of a bar with Parabolic load (I.e. in point with length L)? I found the information on a site, but only I found for uniform load. Someone who ...
11
votes
1answer
146 views

Differential equations with rational functions as solution

I have some families of nonlinear, first order differential equations. When I try to use DSolve, I usually get a mess (if anything at all) in terms of ...
1
vote
0answers
42 views
1
vote
0answers
50 views

Vinculated boundary conditions [closed]

I have a problem in the form: $-y''(x)+V(x)y(x)=0 $ with the initial conditions: $\quad y'(0)=k \ y(0), \quad k=cte$ The $V(x)$ is a model's parameter, for example $V(x)=\frac{6}{\left(x+2\right)^...
4
votes
1answer
53 views
3
votes
0answers
70 views

NDsolve memory leak

Every time I run NDsolve it uses some memory that I am not able to free later. The following is an example code based on the spring equation (Hooke's law) that ...
1
vote
0answers
32 views

Setting different B.C. for different fields in NDSolve

My question regards construction of a PDE solver for several fields, with different type of boundary conditions for several fields. Say I have the following set of equations: $$ \partial_{t}\rho+v\...
1
vote
0answers
52 views

PDE: Specify AccuracyGoal, StepSize, and WorkingPrecision interval-wise [closed]

I am using Mathematica 8. I have two ODEs (in time) and a diffusion PDE (in radius and time) which are all coupled to each other. I solve them using NDSolve by ...
0
votes
1answer
79 views

Lagrangian for Spring-Pendulum [closed]

I solved a Spring-Pendulum System with NDSolve. I tried to plot a graph with the interpolated data but always returns a message "An improperly formatted directive with head Symbol was encountered." <...
1
vote
1answer
46 views

numerical values for the solution of NDEigensystem

I tried to solve Schrödinger equation in 3D box using the NDEigensystem. My code is: ...
2
votes
1answer
132 views

Undershoot/Overshoot Method for this differential equation?

I have tried to solve this equation for some weeks and I am not capable. I have read in articles that it is easy with an undershoot/overshoot method, but I don't know how to do it. $y''+\frac{3}{x}y'-...
0
votes
2answers
95 views

Stiff second order ODE

I am trying to solve numericaly $f''=f^{3}-f$, exact solution is Tanh(x). Problem is numerical solution fails if i coming closer to tanh plateau. StiffnessSwitching method dont help. ...
1
vote
0answers
77 views

Power Spectral Density Plotting [closed]

I am new to signal processing.I am analyzing the connection between the behavior of the Rossler model and its parameter c. \begin{array}{ll} \dot{x} = -y - z \\ \dot{y} = x + 0.2y \\ \label{eq:...
1
vote
1answer
71 views

Nonlinear Markov chain (numerical simulation)

Suppose you have a linear Markov process, and you can write it as x(t+1) = Ax(t). Here x is the vector of values, and A is the transition matrix. Since this is linear, it can be solved analytically, ...
0
votes
1answer
68 views

Stopping NDSolve when encountering stiffness

I am solving a differential equation for different initial conditions using ParametricNDSolveValue. I need to look at the value of the solution at some later point, ...
3
votes
2answers
157 views
0
votes
0answers
80 views

Error - Differential equation //2

This is a follow-up question, since it relates to the solution of a modified version of the original differential equation discussed here: Differential equation: NDSolve::berr I receive an error ...
2
votes
0answers
213 views

DSolve versus DSolveValue [closed]

I've just discovered the new command DSolveValue in Mathematica 10. Is this new command now the preferred instead of DSolve? Is ...
1
vote
0answers
36 views

Speeding up solving nonlinear Schroedinger equation in 3D with NDSolve with periodic boundary conditions

I have a question on speeding up solving nonlinear Schroedinger equation in 3D with NDSolve with periodic boundary conditions. I build the ODE system with NDSolve...
1
vote
0answers
64 views

Differential equation: NDSolve::berr

I'm trying to solve the following differential equation. I'm able to obtain a solution, and that solution looks more or less as how the theory predict it should be. ...
1
vote
2answers
63 views

Logarithmic scale in an ParametricPlot obtained from ODE boundary conditions

How do I plot an ParametricPlot with the x-axis using an logarithmic scale? Since I need to use an ParametricPlot, I can not use the LogLinPlot[] and I also was not able to find any viable Solution in ...
1
vote
1answer
73 views

Differential equation involving history integral

I have not found a solution by using google so I hope I can ask this here. I have an issue with a problem I am trying to solve and I was wondering whether what I am doing is not possible with ...
8
votes
2answers
333 views

Lagrangian to Hamiltonian

I want to go from Lagrangian description to Hamiltonian one. Using the example given by Mathematica I do something like: ...
0
votes
1answer
59 views

Solution of Coupled second-order ODEs and plot the diagram

We have two second-order Coupled differential equations as the followings: $$\left\{\begin{array}{lr} \displaystyle \frac{{{d^2}{y_1}}}{{d{x^2}}} = \{ \frac{{\sqrt {\frac{{1 - {\varepsilon ^2}}}{{{{(...
2
votes
1answer
72 views

Will the solution NDSolveValue finds outside of the region I give it give me bogus results?

I'm using NDSolveValue to solve Laplace's equation for a relatively simple system. I have two rectangles, separated by a small gap, which I define using RegionDifference: ...
1
vote
1answer
84 views

Optimization of the solution to an ODE

Apologies if this is obvious -- I'm very new to Mathematica. I'm trying to minimize the solution to an ODE with respect to a variable. The following code generates the solution to the ODE, ...
4
votes
1answer
324 views

Solving the Frenet Serret equations for non-constant curvature and torsion, obtaining parametric equations

I wish to solve for the curvature and torsion functions $k_1 = \dfrac{1}{1+s^2}, k_2 = \dfrac{s}{1+s^2}$ using the Frenet Serret system and obtain the parametric equations for the curve. I need the ...
0
votes
0answers
76 views

problem with “Infinite expression”, using NDsolve

Im trying to solve an heat equation with NDsolve but i have got a Infinite expression error(1/0). this is the code. ...
3
votes
4answers
417 views

Mathematica not able to confirm its own solution to differential equation

I type the following into Mathematica: DSolve[q''[x] + 2 x/(x^2 - 1) q'[x] - 4*q[x]/(x^2 - 1) == 0, q[x], x] It gives me the result ...
1
vote
1answer
77 views

How to solve different PDE defined in different regions coupled through boundary condition

I would like to solve two different partial differential equations each one defined in a different region and in different coordinates. However the equations are coupled through a boundary condition ...
5
votes
1answer
160 views

Transcritical Bifurcation phase portraits

An example equation for a Transcritical Bifurcations is given by: $$\dfrac{dx}{dt} = f(x, r) = r x - x^2$$ In Mathematica, we can define the function as: ...
2
votes
1answer
82 views

Why does NDSolve and NIntegrate not give the same result? [closed]

I have plotted solution of two equivalent equations one in Integral form (right chart) the other in Differential form (left chart) using NDSolve and NIntegrate but they give me completely different ...
1
vote
0answers
62 views

NDSolve returns solution with single point domain

Thanks to helpful comments from Michael E2 and George2079, I was able to focus in on exactly the source of the issue. With some simplification, I can reduce the problem to: ...
1
vote
1answer
56 views

How can use Table for two functions obtained from NDSolve? [closed]

I have obtained a numerical solution using NDSolve for two functions a(x) and b(x). how do I use Table to make a list of a(x) vs b(x) values. is it simply Table[{a(x),b(x)},{x,0,100}] or should I use ...
1
vote
2answers
75 views

Plotting the InterpolatingFunction from NDSolve [closed]

I want to plot the solution of a differential equation which i solve it numerically with NDSolve. Here's the code: ...
2
votes
2answers
53 views

Difficulty finding roots of an interpolation function from NDSolve

I have been trying to find the point at which one of the solutions of a system of two ODEs crosses zero. I used the method suggested in this answer to a previous question, which seemed to be the most ...
6
votes
1answer
201 views

How to use NDSolve with moving boundary conditions?

So I am trying to solve the movement in space and time of a spreading gravity current. The interface satisfies the following PDE: $ \frac{\partial h}{\partial t} = \frac{\partial}{\partial x}\left(h^...
1
vote
1answer
74 views

NDSolve a system of PDE's when one variable does not have an explicit time derivative

Say I want to solve the following set of PDE's (my actual equations are way more complicated, this is just a simplified example to show the structure): $$\begin{align} \partial_t f(x,t)&=1-g(x,t)\...
1
vote
1answer
83 views

Parametric Plot from ODE using WhenEvent

I am searching for a while now, but I don't seem to be able to find an Answer for my Problem - if I am just not able to search properly, I am really sorry. I Simplified my Problem to the following ...