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

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2
votes
0answers
66 views

How to specify initial condition including integral equations in the case of the dirac equations?

Hi I am trying to solve a system of differential equation with NDSolve. The problem is I have like $3$ (maybe $5$) boundary conditions, but only $2$ differential ...
1
vote
0answers
61 views

Stiffness or Singularity

So trying to run some simulations based on a model I found in literature. I am by no means a Mathematica expert, or a mathematician for that matter. Initial I was getting a ...
4
votes
0answers
66 views

Why do NDSolve and OutputResponse not evaluate non-analytic functions numerically?

test = OutputResponse[TransferFunctionModel[1/(1 + s), s], Exp[-(1/t)], {t, 0, 10}] does not evaluate. If Exp[-(1/t)] is ...
0
votes
0answers
73 views

Nested For loop with NDsolve

I am solving two simple differential equation using NDsolve. ...
3
votes
2answers
219 views

Symbolically solve a system of coupled second order differential equations

I have posted a similar question in another forum where the general consensus seems to suggest that it is not possible to symbolic solve a system of coupled second order differential equations with ...
0
votes
0answers
34 views

How can I draw a bifurcation for the following system [duplicate]

How can I draw a bifurcation for the following system between b and T
1
vote
2answers
679 views

How does one specify Neumann conditions for NDSolve?

I have a series of functions defined in my notebook, and then want to use this to solve a diffusion-reaction type equation. At the moment, something like this works: ...
0
votes
0answers
42 views

Problem with NDSolve and NDSolve::ivone error

I was trying to solve an diffusion-reaction rate model for the oxidation of Silicon (based on the nice paper by Almeida et.al.) with the help of NDSolve. In this model the boundary conditions are a ...
3
votes
1answer
113 views

How to change a parameter dynamically inside NDSolve

I have no idea how to dynamically update a parameter inside NDSolve. For example consider following first-order DE: ...
1
vote
1answer
139 views

To solve Cylinderical PDE

I want to solve this PDE. I have tried to solve it with NDSolve but found error 'Boundary values may only be specified for one independent variable. Initial ...
31
votes
2answers
912 views

Variable naming changes everything

I am having a rather unusual problem I do not understand with Mathematica where renaming one of the variables of my function causes the function to stop "working". Here is the example of the code ...
0
votes
1answer
138 views

Parallel computation of a system of differential equation

I need to solve a system of differential equations which contains, at minimum, ten thousands of differential equations. Actually, I am trying to solve density matrix equation. It's like something ...
4
votes
1answer
114 views

NDSolve - sampling for result during the computation

I am using NDSolve for a Langevin dynamics problem. I want to the know long term behaviour of my system ($t>1$) but it has to be simulated with very small time steps ($dt\sim 10^{-9}$). An example ...
4
votes
0answers
177 views

Modelling Hysteresis with a Differential Equation

I want to implement the bulk ferromagnetic hysteresis model (mostly the Jiles-Atherton Model), see http://drum.lib.umd.edu/bitstream/1903/6043/1/PhD_99-1.pdf page 44 equation (30). The needed ...
5
votes
2answers
481 views

Solving the Helmholtz equation in polar coordinates

I'm trying to (as a simple starter) find the solution to Helmholtz equation in polar coordinates -- I already know what it is and can derive it by hand, but just want to start here before asking ...
8
votes
3answers
620 views

Can Mathematica solve this sort of functional/differential equation?

I am looking for differentiable functions $f$ from the unit interval to itself that satisfy the following equation $\forall\:p \in \left( 0,1 \right)$: $$1-p-f(f(p))-f(p)f'(f(p))=0$$ Is there a way ...
0
votes
0answers
61 views

Plotting the solutions of a system of differential equations on a simplex

I want to solve and plot the solutions of the following system on the triangle simplex: x'[t] == x[t]*(2*x[t] - 2) y'[t] == y[t]*(2*x[t]) z'[t] == z[t]*(2*x[t]) ...
0
votes
1answer
122 views

Infinite expression 1/0.^(1/4) encountered in NDSolve

I am trying to solve very simple system of coupled differential equations using the NDSolve function, but I am getting ...
2
votes
1answer
215 views

Different Poincaré maps for same Equation

I've seen the Wolfram Poincaré example. I'd like to modify this sample in order to have a list of Poincaré maps. In the example the event is captured only when ...
0
votes
0answers
125 views

Calculating the Lyapunov Exponent/Spectrum for the Duffing Oscillator

Some fellow students and I are trying to calculate and plot the Lyapunov spectrum for the Duffing oscillator (currently a test approach). Each of us has Mathematica knowledge based purely on past ...
0
votes
0answers
47 views

Automatic method for NDSolve [duplicate]

How can I understand which method Mathematica automatically chooses to use for numerically solving the following two equations? 1: ...
1
vote
1answer
546 views

shooting method and stifness problem for NDSolve

I'm trying to solve numerically the following differential equation: 1/r[x]^5 + k/Sqrt[1 + r'[x]^2] - (k r[x]r''[x])/(1 + r'[x]^2)^(3/2) == 0 I can set boundary ...
0
votes
0answers
56 views

Derive a PDE from other PDEs

I'm trying to do some symbolic calculation like this: Substitute (11.2) into the last two of equations (11.1) and, in turn, substitute these into the first of equations(11.1), I want to ...
0
votes
1answer
51 views

Dsolve is not solving equation ( 3 system with 2.order diferantial equations) [closed]

I added an image of my equations at the bottom. I dont understand why it is not solving. This is 3 systems with 2.order diferantial equations. I also put my initial conditions. But it is not solving. ...
1
vote
1answer
162 views

Get Cos[2 x] in “Solve”

My goal is to get an analytical solution of x ( $\lambda$ in the problem), when $\epsilon$ (f[x] in the problem) is maximum (use inverse form). I found that if I can use trigonometric identity ...
0
votes
0answers
89 views

NDSolve: Couple ODE and PDE

I am trying to numerically solve an equation with NDSolve, where there is a ODE coupled to a PDE, like the following: ...
0
votes
1answer
99 views

How to work with Interpolating Function?

I'm starting using Mathematica. I have two coupled differential equations and after using NDSolve the output is in the form of a Interpolating Function. I want to Plot the square modulus of one of the ...
0
votes
1answer
67 views

Unable to configure a system of differential equations

My differential equations have been written as ...
0
votes
1answer
126 views

I don't understand ListCorrelate! [closed]

I want to solve a PDE equation (like Schrodinger equation) using finite difference in Mathematica. I don't understand what this code does! ...
0
votes
1answer
136 views

predator prey model with prey refuge

I want to plot the phase diagram of prey predator versus prey refuge to see how the prey refuge influences the population of prey and predator.And this is the system $x'=\alpha ...
-1
votes
1answer
112 views

how to solve this ode problem? [closed]

NDSolve::ndnum: Encountered non-numerical value for a derivative at x \ == 0.`. >>
4
votes
1answer
142 views

Solving a nonlinear, second order d.e. in Mathematica

I am trying to solve the following differential equation $$ s''(x) = \frac{8}{9}s(x) -2s^2(x) + s^3(x), $$ with boundary conditions $s(-30) = 4/3 $ and $s(30)=0$, in Mathematica by using the following ...
1
vote
1answer
107 views

Solution of Coupled Second Order ODEs with Boundary Conditions

D[Tu1[x], {x, 2}] qu - Tu1[x] (fu0 + I w p) == Tou[x] f1 D[T1[x], {x, 2}] q - T1[x] (f0 - b g0 + I w p)== To[x] (f1 - b g1) - g1 For T1 , ...
0
votes
0answers
61 views

Solving systems of equations and derivatives

I am new to Mathematica, and I'm not sure how to solve a system of equations that include differentiation. Given that f and g are differentiable functions: ...
3
votes
1answer
302 views

Solving a differential equation with initial conditions

I want to get a solution to an ordinary differential equation with imposed initial conditions. I'm confused about why my following code doesn't work: ...
1
vote
1answer
169 views

Non-numerical value for a derivative on NDSolve function

I am trying to solve the following system of differential equations: ...
10
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 ...
0
votes
1answer
109 views

DSolve does not give solution

No answer is given when I evaluate the following expression: ...
5
votes
1answer
195 views

VariationalD giving the wrong solution?

EDIT: As pointed out in the comments, VariationalD gives a variational derivative (which I don't want), not a derivative with respect to a function (i.e. ...
1
vote
1answer
114 views

Solution of an ODE in implicit form

For some non-linear ODEs there is only implicit form of solution using DSolve. For example DSolve[(y[x] + x - 1)*y'[x] - y[x] + 2 x + 3 == 0, y[x], x] gives ...
1
vote
0answers
116 views

Runge-Kutta-2 on System

After spending some time using the Mathematica documentation and this Mathematica.SE answer, I implemented the Runge-Kutta-2 routines. I am hoping someone can validate what I did and tell me that it ...
3
votes
1answer
109 views

Polar Differential Equation

I have a polar differential equation (this is the reduced variant) as: $$r' = 0, \theta' = 1$$ I figured out (from previous answers) that I can nicely convert this to Cartesian and use StreamPlot ...
0
votes
1answer
85 views

Plotting the discrete solution to a PDE

So I went through all the grunt work of solving a PDE in discrete form for a research project. Now I have a Temperature solution as a function of time and space: $$ T_{i}^{n+1}=\left( \dfrac ...
1
vote
1answer
63 views

Variable location for intial value in ParametericNDSolve

I am trying to figure out if Mathematica allows a variable location for a known initial value for ParametricNDSolve. I haven't been able to find an example where ...
2
votes
0answers
64 views
0
votes
0answers
48 views

fitting system of ODEs - “part2 of {} does not exist” errod

I'm trying to fit my data to a system of ODEs: x'[t]==a*x[t]+b*y[t] y'[t]==c*y[t]+d*x[t]+e*z[t] z'[t]==f*z[t]+g*y[t] having t,x[t],y[t],z[t]. I followed the code ...
0
votes
1answer
70 views
1
vote
0answers
100 views

BVP system of nonlinear coupled ODEs

Here I am, trying to solve this system of coupled ODEs (up to a minus sign): $ u''=6u^5-(8+4a)u^3+(2+4a)u+\frac{2u((w^2-s)^2+bw)}{(u^2+c)^2}$ $ w''=\frac{4w^3-4bw+b}{u^2+c}$ with the boundary ...
1
vote
1answer
69 views

Discrete sampling of interpolating function returned by NDSolve

When solving an ODE with NDSolve, Mathematica returns an interpolation function. I need a discrete sampling of this function however. Naively, I can write this as (example): ...
0
votes
1answer
100 views

Replacement rules in combination with pure functions to make a change of variables

I have defined my function in this way w = f[r,Θ] ; After some calculations i obtained my results with respect to the previous function. For instance: ...