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

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0
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1answer
324 views

singularity in NDSolve and Table command

We are considering the following equations ...
3
votes
1answer
188 views

Create ParametricFunction object without ParametricNDSolve

Documentation of v9 states that ParametricFunction is generated by ParametricNDSolve and ...
2
votes
1answer
101 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
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0answers
28 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: *Select[Flatten[ ...
3
votes
0answers
210 views

Transform recursion for coefficients into differential equation for generating function

Assume, one is given a linear recursion with polynomial coefficients for a sequence $(a_i)_i$, such as a[i] == i a[i-1] I would like to convert this recursion ...
0
votes
0answers
74 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
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0answers
45 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
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0answers
46 views

Solving Laplace-Beltrami Equation on a Curved Surface [on hold]

Suppose that we have a curved surface $S$, specifically, $S$ is a bump, i.e., $x=\rho\cos(\theta)$, $y=\rho\sin(\theta)$, $z=h\cos^2(\frac{\pi\rho}{2R})$, where $\rho$ runs from $-R$ to $R$ and ...
0
votes
1answer
68 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
390 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
46 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
44 views

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

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
91 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
35 views

Why isn't Mathematica plotting my differential equations? [on hold]

So here are my equations eqns = {x'[t] == a*y[t] - b*x[t] + g, y'[t] == c*x[t] - d*y[t] + m, x[0] == 60937, y[0] == 13797}; Then I solved it with ...
0
votes
0answers
48 views

How to solve Stokes equations with non-vanishing boundary condition on two spheres? [on hold]

I want to solve the Stokes equations for two spherical bodies (some distance apart) with prescribed velocity on their surfaces, in an otherwise static fluid ($\mu$ and $p$ are constants) $$ \left\{ ...
0
votes
0answers
46 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
70 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
0answers
23 views

What is the function derivative [on hold]

What is the function derivative? f'(x)=? what is the way to the answer?
0
votes
1answer
52 views

Unable to configure a system of differential equations

My differential equations have been written as ...
0
votes
0answers
43 views

DSolve failing to solve second-order ODE with two boundary conditons [closed]

I am utilizing Mathematica to solve the following equation: $$y^{''}(x)-5y^{'}(x)+10y(x)=10x $$ The following stated boundary conditions are supplied: $$y(0)=0 \ \ y(1)=100 $$ The following error ...
0
votes
2answers
72 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
1answer
97 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
98 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
113 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 ...
0
votes
0answers
30 views

Multivariable Delay Diff. Equ. with Ndsolve and Nintegrate

I'm trying to simulate the following equation in Mathematica for $u(x,t)$: $$\frac{1}{\alpha} \frac{\partial u(x,t)}{\partial t} = -u + \int_{-\infty}^\infty {\rm d} y w(y) f(u(x-y,t - |y|/v))$$ ...
0
votes
0answers
43 views

Fit a 2 variable ODE to data and estimate parameters [closed]

I am trying fitting on mathematica for the first time. I can do the one variable ones using the sample code. But here I cannot. Can someone help me fit to the data to get answers. I am trying to fit ...
1
vote
1answer
181 views

Error messages from NDSOlve

I am trying to solve a boundary value problem with NDSolve. The code is: ...
1
vote
1answer
437 views

Integro-differential eqn with double integral

I am looking at the following variation of a integro-differential, with y[0]=1. The output is not great, any solutions to this? ...
-1
votes
0answers
41 views

Numerical solution of an ODE with a singularity at the initial value

I have a differential equation: (c^2-y[x]^2)*y'[x] - (a+b)*y[x]^2 + ((2/x)*c^2)*y[x] - c^2*b = 0 with the initial condition ...
1
vote
1answer
71 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
53 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: ...
0
votes
1answer
58 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
229 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
63 views

Non-numerical value for a derivative on NDSolve function

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

DSolve does not give solution

No answer is given when I evaluate the following expression: ...
5
votes
1answer
171 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
85 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
89 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
86 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
75 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
56 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
51 views
0
votes
0answers
24 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
0answers
20 views

How do you find the general solution to a higher order nonhomogeneous differential equation? [migrated]

Find the general solution: y'''-3y''+3y'-y=t*exp(t) <-3rd Order y''''-2y'''+2y''=t*exp(t)*cos(t) <-4th Order
0
votes
1answer
57 views
1
vote
0answers
56 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 ...
0
votes
1answer
43 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
82 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: ...