Tagged Questions

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

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1
vote
1answer
152 views

Bilateral Laplace Transform in Mathematica (to be used with Moment Generating Functions)?

I am trying to solve a linear ODE for a Kolmogorov forward equation to get a stationary distribution of a random variable. The easiest approach may be to transform the ODE with a two-sided Laplace ...
0
votes
0answers
84 views

Problem with using the results of ParametricNDSolve in a ParametricPlot3D

I new to Mathematica and I have a problem with certain equations. I want to plot a trajectory in spherical coordinates given by the equations: ...
2
votes
1answer
123 views

Why do identifiers of the form ${\tt c}k\$nnn$ appear in the rules returned by my function?

I want to define a function, PolynomialInterpolation to find the coefficients of a polynomial interpolation function. My trial is as shown below: ...
0
votes
0answers
67 views

Solving an ODE, where the coefficients are implicit functions of time, not in closed form [duplicate]

I have an ODE, say of the first order for simplicity, and of the form, $A.x'[t] =B$. The coefficients are functions of time and x[t], not in closed form. I can define the coefficients, $A$ and $B$, ...
2
votes
2answers
156 views

Find minimum value of function which calls NDsolve [duplicate]

I have defined a function which takes a coefficient for a differential equation as an argument, solves the differential equation with NDSolve, and returns the value of the solution at time t=10. I can ...
1
vote
1answer
132 views

How to choose a solution of a differential equation?

I am trying to solve the following differential equation: ...
2
votes
0answers
90 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
70 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
1answer
94 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
35 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
3
votes
2answers
303 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
50 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 ...
0
votes
1answer
262 views

Parallel computation of NDSolve and a problem

I used this code to solve a system of differential equations: ...
1
vote
1answer
79 views

How to study the sign of an expression including a function, with conditions on the function?

I'm trying to study the sign of an expression, having information on some of my parameters. I don't know how to code these conditions. For example, I want to know when this expression: ...
4
votes
1answer
141 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
158 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 ...
0
votes
1answer
190 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
0answers
222 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 ...
6
votes
2answers
667 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 ...
4
votes
1answer
129 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 ...
0
votes
0answers
74 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]) ...
2
votes
3answers
383 views

DSolve will not apply assumption m ∈ Integers

I am trying to solve a linear second order ODE using DSolve which involves an arbitrary integer m. ...
2
votes
1answer
193 views

Understanding of method for NDSolve

I used automatic method for NDSolve. Then I asked myself - which method Mathemathica prefered? I got an answer for this question on this forum, that I need to use: ...
2
votes
1answer
280 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
49 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: ...
0
votes
0answers
153 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
1answer
58 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. ...
0
votes
1answer
221 views

Solving System of Nonlinear with Three Differential Equations

I've been trying to solve a system of nonlinear differential equation, but the conditions are a bit weird. Two of the differentials equate to the same equation, but have different boundary ...
1
vote
1answer
232 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
57 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
0answers
123 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
122 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
71 views

Unable to configure a system of differential equations

My differential equations have been written as ...
0
votes
1answer
156 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
183 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 ...
0
votes
0answers
66 views

Multivariable Delay Diff. Equ. with Ndsolve and Nintegrate

I'm trying to simulate the following equation in Mathematica for $u(x,t)$: $$\frac{1}{\alpha} \frac{\partial u(x,t)}{\partial t} = -u + \int_{-\infty}^\infty {\rm d} y w(x-y) f(u(y,t - |y|/v))$$ ...
4
votes
1answer
160 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 ...
2
votes
3answers
316 views

Constraining function found by NDSolve to stay positive

I am trying to constrain my variables in NDSolve so that they stay positive for the integration interval. Is is possible to do that? Using Assumptions as in ...
0
votes
0answers
72 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: ...
1
vote
1answer
132 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
224 views

Problem with Plot and ParametricNDSolve

This is my first question on this site, I hope it is written in an understandable way. Let's start. My aim is to plot a certain parametric region, with $x$ and $y$ coordinates given by the following ...
3
votes
1answer
376 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
360 views

Non-numerical value for a derivative on NDSolve function

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

DSolve does not give solution

No answer is given when I evaluate the following expression: ...
1
vote
0answers
140 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 ...
1
vote
1answer
146 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 ...
3
votes
1answer
133 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 ...
1
vote
1answer
66 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
70 views

Locate Blow-up in NDSolve with Whenevent

At some point I get this error: ...
0
votes
0answers
66 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 ...