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

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1
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1answer
301 views

Problem using NDSolve

This might be some simple mistake, but I am running out of ideas. I am trying to fit an ODE system to some data. This error keeps appearing NDSolve::nlnum: "The function value {0.299812 - ...
9
votes
3answers
2k views

Solving a time-dependent Schroedinger equation

I want to solve the time-dependent Schroedinger equation: $$ i\partial_t \psi(t) = H(t)\psi(t) $$ for matrix, time-dependent $H(t)$ and vector $\psi$. What is an efficient way of doing this so ...
2
votes
1answer
199 views

ParametricPlot3D doesn't appear

Here I have one simple system solvable with NDSolve. I don't know why ParametricPlot3D doesn't present trajectory in space. I have solutions for x[t], y[t] and z[t] ...
0
votes
1answer
283 views

Applying l'Hôpital's Rule to NDSolve with Piecewise Function

OK, so I've been working on this problem for over a week and it's driving me crazy. I'm trying to solve a system of two differential equations in $x(t)$ and $y(t)$ using a "time-elimination method," ...
4
votes
1answer
102 views

How can I highlight the vanishing-partials in an interactive 3D plot?

I am using Manipulate and Plot3D to plot a function with two real variables and two extra parameters. ...
1
vote
2answers
472 views

Weird NDSolve behavior with Piecewise (MMA9)

NDSolve in Mathematica 9.0.0 (MacOS) is behaving strangely with a piecewise right hand side. The following code (a simplified version of my real problem): ...
1
vote
1answer
469 views

How to calculate a gradient at x=0?

I am solving a second order differential equation for n[x]. I solved it with both DSolve and NDSolve. A plot of n as a function of x looks great. Than I want to calculate a gradient of n[x] at a ...
1
vote
1answer
203 views

Troubleshooting an NDSolve::ndfdmc error message

Τhe following code ...
1
vote
2answers
410 views
1
vote
1answer
151 views

Solving a system consisting of an ODE and a non-differential equation

I would like to solve the following system of equations: y'[t] == x[t]*y[t] - x[t]; 10 == x[t]*y[t]/(x[t] + y[t]) + x[t]/(x[t] + y[t]^2) Is there any way to ...
2
votes
2answers
260 views

Solving and plotting ODEs while varying one of the initial conditions

How can I vary an initial condition in the numerical solution of a system of ODEs and then make a 3D plot of the solution space with that condition as one of the variables. ...
15
votes
1answer
951 views

2D Heat equation: inconsistent boundary and initial conditions

I'm attempting to use NDSolve on a 2D boundary value problem with initial conditions. Upon running my code, I get the following message: "NDSolve::ibcinc: Warning: Boundary and initial conditions are ...
5
votes
2answers
284 views

Symmetry-finding packages

Where can I find the most up-to-date or whatever you consider to be the most useful symmetry-finding package for differential equations? I do not intend to restrict to, but would like to include ...
2
votes
2answers
539 views

Returning a function from a Module [duplicate]

I'm having problems working with the output from DSolve whilst in a module. To handle the result outside a module typically I would do something like ...
0
votes
1answer
155 views

Evaluating derivatives for use in solve

I need to evaluate the derivative of a function. My function looks like approx[vector_, x_] := Sum[vector[[n]]*Basis[n - 1, x], {n, 1, Length[vector]}] and I'm ...
2
votes
1answer
305 views

Intermediate variables in NDSolve

I'm interested in using NDSolve as an integrator for a system of differential equations that looks like the following: ...
0
votes
0answers
180 views

NDSolve equations contain solution from solving cubic equations [on hold]

I'm having trouble using NDSolve to solve equations that were obtained from solving cubic equations. In my problem, I first obtained 6 functions (ca1, ...
2
votes
3answers
870 views

How to calculate partial derivative of an unknown function

How can I force Mathematica to calculate symbolically the partial derivative of a function u[x,y] with respect to a variable ...
3
votes
1answer
278 views

NDSolve problem with matrix valued function

I got a strange problem when using NDSolve to solve a matrix value function σ[t] = {{σx[t], σxy[t]}, {σyx[t], σy[t]}} when I ...
5
votes
1answer
946 views

Is it possible to do vector calculus in Mathematica?

I am trying to rearrange and manipulate some vector differential equations in Mathematica. As far as I understand you have to tell Mathematica that a variable is a vector by specifying the components ...
3
votes
2answers
199 views

How can I get WhenEvent to recognize criterion I specify?

Using NDSolve I want to solve a differential equation till a quantity which is a function of the dependent variables reaches a certain value. My functions and criteria are complicated, but I am able ...
-2
votes
1answer
185 views

Problem with solving a differential equation [closed]

I need to solve the following differential equation: NDSolve[{R[r, t], R[r, 0] == r/1000}, R, {t, 0, 30}, {r, 1, 30}] Where ...
0
votes
1answer
113 views

Differential Equation help

I have a differential equation that looks like this: ...
1
vote
2answers
189 views

Discard ODE singular solutions with Mathematica?

The solution for a homogeneous second order linear ODE is generally a constant times one function plus another constant times a different function. Sometimes one of the solution functions is ...
0
votes
1answer
351 views

Setting boundary values of a second order differential equation

Not sure what is wrong with the boundary conditions for this problem: ...
0
votes
1answer
176 views

Subtracting results of NDSolve

I have 2 variables as a results from the NDSolve[] which are ua and uw. This is how I do it, ...
13
votes
3answers
574 views

How to splice together several instances of InterpolatingFunction?

I have a set of InterpolatingFunction returned by NDSolve which are valid over different (but overall continuous) domains. How ...
6
votes
2answers
644 views

How do I solve a PDE with a strange boundary condition?

How do I solve the PDE with boundary value like this $$u(t,x,y)=0, \textrm{when } F(x,y)=0$$ using DSolve? As a specific example, I want to solve heat equation $$\frac{\partial u}{\partial ...
2
votes
1answer
177 views

Using NDSolve solution as initial condition for another NDSolve

I have solved a PDE numerically using NDSolve, and I now need to be able to use that solution as an initial condition for another ...
0
votes
0answers
126 views

Need conditions for DSolve

If I have differential equation of fourth order with four solutions $\alpha _1,\alpha _2,-\alpha _1,-\alpha _2 $ where we have appearing the solutions in the form $e^{\text{$i\alpha $}_1 ...
0
votes
1answer
391 views

How to understand and use DSolve solution

This equation is simple to DSolve in Mathematica, but I don't know how to use and understand solution. ...
4
votes
2answers
1k views

How do I plot a solution of a differential equation?

I am having trouble generating a plot for a solution to my differential equations. I always end up with just blank axes. ...
1
vote
1answer
167 views

How to transform equation

Is there any possible way to write this equation of 4th order as a system of two diff equations of second order with two new variables and to do that automatically? statespace command is transforming ...
4
votes
1answer
335 views
5
votes
0answers
324 views

Modeling neural excitation with a non-linear differential equation

I think I have a special problem and I am not sure how to search for an answer, so I thought I would try here. I am working with the so called FitzHugh-Nagumo model which describes very simple ...
1
vote
1answer
163 views

Finding parameters for first positive root of solution to differential equation to be equal to a desired value

I have a differential equation with parameters. The objective is to vary the parameters such that the first positive root of the solution is equal to a desired value ...
0
votes
1answer
309 views

DSolve output - understanding how to extract result

I'm a little confused with how to use the output from DSolve. The following works ...
0
votes
1answer
558 views

Decoupling system of differential equations

Here I have one task and it is preparation for small exam. I solved it by hand for first case 1), but I need to check it in $Mathematica$ and to try to implement it for both cases 1) and 2) ...
10
votes
1answer
455 views

NDSolve Differential Equation Error

I am trying to solve the following differential equation- ...
0
votes
1answer
331 views

Boundary Value Problem

I have to solve this boundary value problem: $$\frac{\mathrm{d}e_{3x}}{\mathrm{d}l}=(M_0+F_{0z}x-F_{0x}z)e_{3z}$$ $$\frac{\mathrm{d}e_{3z}}{\mathrm{d}l}=-(M_0+F_{0z}x-F_{0x}z)e_{3x}$$ ...
0
votes
1answer
234 views

Solving the wave PDE using the Fourier method

I am trying to solve the wave PDE using the Fourier method and I need to animate the plots of the partial sum of order 45 -- U45(x,t) with initial conditions U45(x,t0), {t0, 0, 12, .2}. I am ...
3
votes
1answer
1k views

How can I solve this PDE with initial conditions?

I wish to solve the following second order partial differential equation $$u_{tt}=c^2 u_{xx}$$ with the initial conditions $$u(x,0)=e^x,\quad u_t(x,0)=\sin x$$ In Mathematica, I evaluated the ...
2
votes
0answers
449 views

ParametricNDSolveValue or NDSolve + fitting

I have been trying to find the value for the parameter kestim that yields the best fit of a model to some data points. datac has ...
1
vote
1answer
397 views

Optimizing the fitting of Ordinary Differential Equation(NDsolve) involving interpolation functions

I am a newbie to this forum. I am trying to use NDsolve to solve some ODEs involving the interpolation function. Then, I will compare the fitted curve and data to determine the ODE coefficients. ...
0
votes
0answers
94 views

A good choice to find solutions of ODE

In order to rephrase the question. I would ask you to take a look at the following problem: I have this system of ODE: $$ \begin{cases} \dot{x}(t)= x(t)[r_1(t) -b_1(t)x(t- \tau(t)) - c_1(t)y^m(t)] ...
-1
votes
1answer
161 views

Some Problem with WhenEvent!

Anyone knows what's the problem with the following code and how can I fix it? I am not sure that I wrote the WhenEvent section correctly. By the way, I want to solve the equations and then plot y vs. ...
4
votes
3answers
1k views

Lyapunov Exponent

Does anyone know a (simple) Mathematica code for computing the Lyuponov Exponent for the Rossler System? Thank you Rossler System: ...
3
votes
0answers
101 views

Symbolic solution to ODE, pure InverseFunction not evaluated

I'm new to Mathematica and I don't understand why in the solution of the following ODE, the #1 in the pure function is not immediately replaced by the corresponding ...
3
votes
1answer
666 views

How to correctly use DSolve when the force is an impulse (dirac delta) and initial conditions are not zero

DSolve (and NDSolve) return different and unexpected solution to differential equation when the input is an impulse. This is ...
1
vote
1answer
277 views

NDSolve for PDE with discontinuous initial/terminal condition

I have an issue with NDSolve for the case of a PDE with discontinuous initial/terminal condition. Consider the PDE solution ...