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

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0
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0answers
118 views

NDSolve :: ndode error while solving an coupled ODEs

I have a scenario where in trying to solve for the ground-state of a Hamiltonian, I require to be able to solve some coupled differential equations. Prior to this I have already set k=1 and Δ=5 $$ ...
0
votes
1answer
976 views

how to solve second order nonlinear coupled differential equations using NDSolve with hyperbolic function

i have to solve some solitons scattering through this coupled equations. i need to get two different graph, but still the graph did not come out. and also the equations quite complicated containing ...
1
vote
2answers
607 views

How to make Mathematica use the chain rule?

Lets say I have the following PDE: $$x^2 u_{xx} - u_{yy} + u_y = 0$$ And I have the following change of variables: $$ s(x,y) = x e^y \, \, \, , \, \, t(x,y) = x e^{-y}$$ How can I use Mathematica ...
6
votes
3answers
506 views

RK4 Gravity Simulator

I have the following RK4 solver which splits the two 2nd order ODEs, used to calculate x and y positions under the influence of a gravitating body where $$x''(t)=\frac{G m ...
2
votes
1answer
298 views

Euler's method for a 2nd order ODE

This is my first post on this site. Also, I'm new to Mathematica. I'm trying to solve my first problem with Mathematica. It's about solving a 2nd order differential equation. I dont have the explicit ...
8
votes
1answer
891 views

Schrödinger eigenvalue problem in two dimensions (Harmonic Oscillator)

I read here the discussion about how to solve a one-dimensional eigenvalue problem. I am wondering, how can one generalize these methods to two dimensions? For example: ...
0
votes
2answers
205 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
902 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 ...
2
votes
0answers
363 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
102 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
340 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
539 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
267 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
704 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
62 views

Error message from NDSolve using WhenEvent

I am working with the following NDSolve expression: ...
3
votes
1answer
267 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
202 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
1k 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
113 views

why I can not find the correct derivative with D

the coupled ODE is ...
0
votes
1answer
238 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
184 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
2k 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
393 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
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0answers
80 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
122 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
119 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
330 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
44 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: ...
3
votes
1answer
538 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
137 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
70 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
122 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
83 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 : ...
0
votes
1answer
94 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 ...
19
votes
2answers
2k 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
178 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 ...
0
votes
0answers
103 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
758 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: ...
4
votes
2answers
431 views

Bilateral Laplace Transform

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 ...
2
votes
1answer
126 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
68 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
292 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
174 views

How to choose a solution of a differential equation?

I am trying to solve the following differential equation: ...
2
votes
0answers
121 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 ...
4
votes
1answer
148 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 ...
1
vote
1answer
173 views

How to check a solution of a partial differential equations?

Here is a system which Maple can solve, but Mathematica cannot. ...
3
votes
2answers
684 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
1answer
473 views

Parallel computation of NDSolve and a problem

I used this code to solve a system of differential equations: ...
1
vote
1answer
125 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: ...
6
votes
1answer
260 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: ...