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

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-1
votes
2answers
78 views

Solving partial differential equation with DSolve does not give a result [closed]

I am trying to solve the equation: $-(d^2/dx^2+d^2/dy^2)\psi+(x^2+y^2-2)\psi=0$ Here, is my code: ...
0
votes
2answers
94 views

Eigenvalue problem and plotting its eigenfunctions [duplicate]

How many different ways can one solve an eigenvalue problem and plot its corresponding eigenfunctions in Mathematica? For example for Harmonic Oscillator? Which one is the most accurate one? Thanks ...
1
vote
0answers
63 views

Solving two-component two-dimensional differential Equation with NDSolve (Brusselator Model)

I'm trying to solve a two-component two-dimensional reaction-diffusion differential equation system with Mathematica. The background of the model is the so called "Brusselator Model" where one can ...
0
votes
1answer
94 views

Solving a differential Equation

I am trying to solve -D[((α + γ/2)*a + β/(2*a) - R*a^3)*p[a], a] + 0.5*D[(γ*a^2 + β)*p[a], {a, 2}] == 0 with DSolve, but it ...
0
votes
0answers
85 views

NDSolve gives wrong results for “stiff system”

I have a physical problem in which I want to solve for c[e] as a function of e, where c is ...
0
votes
3answers
157 views

Solving One Equation with Two Variables

I am trying to solve an equation with two variables. It is the last step in the process of using the method of undetermined coefficients to solve a nonhomogeneous differential equation. The equation ...
0
votes
1answer
90 views

Solving for the time-evolution operator in a periodically driven system

I am looking at the Hamiltonian $$H(t)=\begin{pmatrix} 0 & e^{i\Omega t}\\ e^{-i\Omega t}& 0\end{pmatrix}$$ I am trying to solve for the unitary operator $U(t,0)=\mathcal{T}\exp(-i\int_0^t ...
1
vote
1answer
135 views

Solving a complex-valued differential equation with NDSolve

I am trying to solve $dx/dt=\sqrt{1+(ix)^{1.8}}$ for initial condition $x[0] =-0.9877 + i 0.1563$, where $x$ is a complex variable. I would like to plot the imaginary part of the solution versus the ...
0
votes
1answer
37 views

Error message from NDSolve using WhenEvent

I am working with the following NDSolve expression: ...
2
votes
1answer
121 views

Differential Equation in Complex Plane and Parametric Plot

I would like to solve $dx/dt=\sqrt{1 + (I x)^3}$, where x is complex, for some initial condition like $1 - 5 I$ and plot the imaginary part of the solution versus the real part. (A somewhat similar ...
1
vote
2answers
121 views

Complex differential equation

I want to solve $dx/dt=\sqrt{(1-x^2)}$, where $x$ is complex. When I solve it by hand and analytically for some initial value and draw the imaginary part versus the real part, I obtain an ellipse, as ...
1
vote
1answer
127 views

Runge-Kutta 2nd Order ODE Solver

Suppose I have a 2nd order ODE of the form y''(t) = 1/y with y(0) = 0 and y'(0) = 10, and ...
0
votes
1answer
96 views
0
votes
2answers
103 views

Plot slope field in Mathematica for a difficult differential equation

I am trying to plot slope field for $\ddot{a}(t)$ for this differential equation but I don't know how to $\frac{d}{dt}\ddot{a}(t)=2\frac{\dot{a}(t)}{a(t)}\ddot{a}(t)$ I want to show that already ...
2
votes
1answer
86 views

Finding the roots of a function with a parameter

I am using a differential equation method for finding the roots of a function. My function is much more complicated but I can illustrate my problem with a trivial example. The problem occurs when ...
4
votes
3answers
285 views

Creating a 3D List Line Plot From Discrete Points

Given the following Runge-Kutta ODE solver and the graphical output below, how do I get a 3D line plot instead of a 3D point plot? I see that there is no ListLinePlot3D function, so I thought it might ...
1
vote
2answers
82 views

How to set initial guess in NDSolve

I'm trying to solve a BVP using NDSolve and I want to impose the starting initial guess. I googled and looked at the help, but I couldn't find this option. ...
0
votes
0answers
62 views

System of differential equations - solving for a constant

I will reformulate my question in the hopes it will be more intelligible. First, I defined the functions: ...
1
vote
1answer
90 views

Solving differential equation - initial condition

I want to solve the differential equation: DSolve[{R''[ρ] + 2 /ρ R'[ρ] + (1 - (l (l + 1))/ρ^2) R[ρ] == 0}, R[ρ], ρ] This works fine and outputs: ...
0
votes
0answers
63 views

How can I get the time steps chosen by NDSolve when the Method -> “ExplicitRungeKutta” option is given?

I am trying to solve an ODE with NDSolve using the "ExplicitRungeKutta" method. I need to know exactly which time steps ...
0
votes
1answer
77 views

How do I fit NDSolve result to experimental data? [duplicate]

I have two coupled ordinary differential equations which I solve numerically in Mathematica, but now I want to fit the solution with experimental data. I do following, (the experimental data ...
0
votes
0answers
42 views

How to use results of Dsolve and get derivative of that? [duplicate]

How can I use the result of DSolve and differentiate it' result? Here for example I want to, first find urf from solving: ...
0
votes
0answers
42 views

Calculate inverse laplace transform by integration with four singular points?

I have a function U[s,x] to do inverse Laplace transform for analytical solution, as following ...
2
votes
1answer
72 views

NDSolve::ndsz problem

I'm using NDSolve to solve a set of coupled differential equation which depend on a variable x. I noticed that when I set the range of x from a small value to a large value, I obtain solutions. But ...
0
votes
1answer
43 views

Using variable with delay in WhenEvents in NDSolve

I have a system of differential equations which is solved correctly. However, I want to trigger two events, one of which depends on the "time elapsed" after of the first event trigger. Is it possible ...
0
votes
0answers
58 views

Solving a system of three differential equations

I'm trying to create this coloured graph which I'm going to animate, but I'm stuck with solving a system of three differential equations: ...
0
votes
1answer
105 views

Better way to check conservation in NDSolve

The partial differential equation in the NDSolve below is conservative (by construction) of $\int_{-1}^{+1} p(t,z)\ dz$ for all $t$. ...
0
votes
0answers
49 views

Can't Solve a system of differential equations, Solve takes too long

My question is probably not really interesting but I really need help on this because I won't have access to a more powerful computer. So my model contains 7 equations : ...
1
vote
0answers
37 views

RSolve works slow and does not give an analytical solution for solving high order linear difference equations

RSolve@@{{a[n]-a[n-10]==101}~Join~Table[a[i+1]==101+10i,{i,0,9}],a[n],n} I want to get the exact form of general formulas, but ...
6
votes
1answer
480 views

Animation of double pendulum

Sadly, I am a completely newbie. I am studying Physics and in our theoretical physics class we got the task to solve the double pendulum using Mathematica. We just got the program, but no introduction ...
0
votes
1answer
130 views

Zooming into Parametric Animation Plot that Uses InterpolatingFunctions

I have an interplanetary trajectory solver that calculates a spacecraft route from Earth to Mars, and I am trying to zoom into the spacecraft when it reaches its Mars intercept orbit but am having ...
1
vote
0answers
45 views

Combined Elliptic-Parabolic PDE in 1D [closed]

Here is an example of solving a system of parabolic and elliptic PDE: http://reference.wolfram.com/mathematica/tutorial/NDSolveDAE.html (see the subsection "Combined Elliptic-Parabolic PDE in 1D"). ...
0
votes
0answers
47 views

PDE combined with ODE 1D

I try to solve the following system of PDE coupled with ODE: $$\theta_t - a\theta_{xx} + b\kappa_a(\theta^4-\varphi)=0,$$ $$-\alpha\varphi_{xx} + \kappa_a(\varphi - \theta^4) = 0,$$ $$-a\theta_x + ...
11
votes
3answers
410 views

Determine frequency of oscillations

I am wondering how I could determine the frequency of oscillations of a differential model equation? How could I find the frequency from this example given in Mathematica Documentation: ...
0
votes
0answers
43 views

Ideas for NDSolve?

I'm currently trying to find a numerical solution to a differential equation of the form: D[W[X], {X, 4}] ==(-(1/(delta + G - (G X)/L)^2) + 1/(delta + (G X)/L)^2) ...
1
vote
1answer
90 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
68 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: ...
0
votes
0answers
76 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: ...
2
votes
2answers
114 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
108 views

How to choose a solution of a differential equation?

I am trying to solve the following differential equation: ...
2
votes
0answers
62 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
58 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
63 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
66 views

Nested For loop with NDsolve

I am solving two simple differential equation using NDsolve. ...
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
3
votes
2answers
200 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
40 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
167 views

Parallel computation of NDSolve and a problem

I used this code to solve a system of differential equations: ...
1
vote
1answer
75 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: ...
3
votes
1answer
104 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: ...