Questions tagged [differential-equations]

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

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1answer
39 views

How to check numerical values on a plot? [closed]

Suppose we have the model: ...
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104 views

How to numerically solve this system?

Our system: \begin{align} \dot S &= \mu -\beta_1 S I_2 -\beta_2 S J-\beta_3 S A - \nu S\\[2ex] \dot {I_1} &= p \beta_1 S I_1 +q \beta_2 S J +r \beta_3 S A + \xi_1 J- b_1 I_1 \\[2ex] \dot{...
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59 views

Optimization for numerical integration of Airy function and using NIntegrate inside NDSolve

Sorry for the long post. I need to integrate a function which uses the trajectory data given by the Lorentz force equation. We have the electromagnetic field: $$ \vec{E}=E_0 \cos{\omega(t+\bar{z})}\...
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1answer
97 views

Solving a system of differential-algebraic equations

I am trying to solve a coupled system of differential-algebraic equations as follows. First define a list of 6 equations ...
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1answer
27 views

NDSolve::ndnum: Encountered non-numerical value for a derivative at t == 0.` [closed]

I am unable to get a numerical solution to a system of two coupled second order differential equations using NDSolve. These coupled ODEs are for a physical phenomenon known as a looping pendulum, and ...
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1answer
82 views

How to plot a smooth LogLogPlot of an oscillatory function having damping

I am trying to plot a damping solution with LogLogPlot ...
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1answer
144 views

how can I solve this logarithmic equation?

I've tried NSolve, Solve and Reduce for solving this equation but non of them worked. would you please help me? ...
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44 views

Are these solutions correct using `AsymptoticDSolveValue`? Less::nord: Invalid comparison with I attempted

Should one worry about correctness of these solutions due to the messages they generate? Or can one safely ignore these messages? Example 1 ...
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1answer
101 views

Orbit integrator / Keplerian orbit

I want to integrate a circular Keplerian orbit with GM = 1, a = 1 over 100 orbital periods. But the thing is that I can only make the Orbit change when I change a. And the Orbit remains the same when ...
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2answers
149 views

Numerical solution of the 2D-spatial nonlinear Allen equation

I would like to solve the 2D-spatial Allen equation in rectangular coordinate, which is a nonlinear reaction-diffusion PDE of the type $$\partial_{t}u=\epsilon(\partial_{xx}+\partial_{yy})u + u - u^{3}...
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2answers
44 views

Error complex function ERFI(X): looking for alternative function representations?

I have some analytical results from a physics problem, where the Mathematica gives the results in terms of complex error function. I would like to explore another function representation using ...
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56 views

How to re write the solution to this pde [closed]

I have this equation solved: ...
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1answer
81 views

Dog-Owner problem(pursuit curve)

A dog in the coordinate system starts from the origin along the x-axis with vk=1m/s speed. The owner starts from the (0,1) point running towards the direction of the dog with vg=2m/s speed.Show the ...
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Using NDSolve with Interpolated Functions

I'm trying to run code designed to solve for a particle's spin given its velocity. The particle is in a rotating fluid with (in this case) parallel external electric & magnetic fields. The code, ...
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1answer
103 views

Lotka-Volterra in mathematica

I have to solve the next problem: We know that a=b=c=d=1 and x0=2,y0=3,q=0.2,On the t=[0,20] interval there is no fishing but on the t=[20,40] interval there is.Show the adequate trajectory(the first ...
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2answers
116 views

Poincaré section for non-autonomous logistic equation with periodic harvesting

I'd like to plot the Poincaré section based on the problem from here: see exercise 8.1 Given that the standard logistic equation with harvesting function is $$\dfrac{dx}{dt} = ax(1 - x) - h (1 + \sin{...
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1answer
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Solving Second Order Differential Equation with Discrete Time Data

Given the Second Order Differential Equation: $$ m\ddot{x}+c\dot{x}+kx = \mathrm{F}_{external}^{} $$ where $ m, c, k $ are constants and $\mathrm{F}_{external}^{}$ is buffer of external force taken ...
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2answers
63 views

Getting ODE solution in forms other than exponential or as a pure function

I'm new to Mathematica and trying to solve some ODE's through it. But, whenever I try solving these ODE's I get pure functions as solutions with exponents only. Here's a pic for example. Now, if I do ...
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1answer
71 views

optimization with multiple parameters and differential equations

There might be some relevant questions and answers, but I couldn't complete my code by myself just by reading them. Sorry that I am very new to Mathematica and my question could be a bit rough and not ...
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1answer
108 views

Finite difference method for solving coupled differential equations

I am trying to solve the following coupled differential equations: $\dot{c}_{1}(t)=-\int_0^t \alpha_{1}(t,s)c_{1}(s)+\beta_{1}(t,s)c_{2}(s)\,ds-\frac{i}{\hbar}\lambda c_2(t)e^{+i(\omega_1-\omega_2) t}$...
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102 views

How do i solve two coupled nonlinear PDEs through Mathematica?

these are two relativistic fluid governing equations, ∂_t (γe)+∂_x(γev)=0 γ∂_t(γv)+∂_x[(γv)^2/2]=-(C/(1+C))*∂_x[log(e)] where γ=1/sqrt(1-v^2) is Lorentz factor, <...
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1answer
54 views

DSolve Second Order Differential Equation with One Boundary Condition [closed]

So I set up my singular perturbation problem after change of variables for equation and boundary condition. But when using DSolve for the analytical solution, there's always a 1/2 in front of it. Can ...
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2answers
178 views

NDSOLVE mathematica fluid mechanics

i have made mathematica code for equation 16 . . using it 1st time and facing a lot of errors . . can some guide about the problem. . guidance according to FLUID MECHANICS field would be great ...
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1answer
34 views

DSolve subject to [closed]

I want to compute two differential equations with subject to conditions. My solution: ...
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0answers
92 views

I want MathLie setup for mathematica [duplicate]

I tried to find Math lie in Mathematica but I didn't find setup. Can anyone share Math lie setup for Mathematica?
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NDSolve::ndsz error: singularity or stiff system suspected | Coupled ODEs [closed]

I am new to Mathematica. Trying to solve the below coupled-ODEs (eqnA, eqnB, eqnC). However, getting error NDSolve::ndsz: At x == 0.8849324488967629`, step size is effectively zero; singularity or ...
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1answer
152 views

Calculating the 3D Vector field of a permanent magnet with FEM

trying to calculate the magnetic field of a permanent magnet using the finite element method I struggle setting up the equation system properly. In the end I want to be able to calculate the magnetic ...
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2answers
154 views

Why the difference in fundamental solutions?

Finding a fundamental solution of a linear differential operator $f''-c^2f$, I try in 12.3.1 on Windows 10 DSolve[f''[x] - c^2*f[x] == DiracDelta[x - y], f[x], x] ...
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solve pde with moving top boundary

I am trying to solve this pde (1D diffusion with source term) with a top boundary that moves over time noted as L0[t]. The NDsolve works when L0=constant, but here the top boundary changes in height ...
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1answer
115 views

Simple hybrid ODE cannot be solved symbolically

Mathematica solves the following very simple hybrid ODE without any problem: DSolve[{x'[t] == 1, x[0] == 0, WhenEvent[x[t] == 2, x[t] -> 0]}, x[t], {t, 0, 5}] ...
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50 views

Solution to differential equation only starts at random times (numerical error?)

I am solving a set of differential equations with an oscillatory forcing (square wave). Instead of the solution starting to oscillate immediately it stays still until some time. That varies with small ...
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1answer
84 views

The heat equation on the intervall [0,1] with Robin Boundary

I have the heat equation on the invervall $[0,1]$, therefore I define heqn = D[u[x, t], t] == D[u[x, t], {x, 2}]; and I define my initial data which can be boring, ...
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2answers
84 views

How to realize NDSolve by NSolve with the implicit constraint equations?

Daniel post the amazing code to realize numerical integrators, I think it is useful to the kind of one-step explicit equation like x[k+1]-x[k]== constant_number. In ...
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36 views

Fitting coupled ODEs on data

I'm learning how to fit a system of two ODEs to data. The dataset is in the form dataset=Transpose[{time,datax,datay}] {{0.,0.,0.},{0.1,0.283791,0.0949328},...} ...
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1answer
53 views

How to realize NDSolve by Solve?

I want realize the NDSolve by Solve,so I read some numerical integration resource. In common setting, ODEs can be solve by Euler ...
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32 views

Converting 1D map into first order differential equation for bifurcation diagram code

I have existing code to plot bifurcation diagram for coupled first order differential equations. It seems to work for coupled differential equations. To test the code further, I use the simplest ...
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1answer
60 views

Plot When y axis data very small

I use NDSolve solve the motion equation of a dynamic system. and When I plot the energy of the dynamic system, I find the y axis data is very small, I have take ...
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1answer
51 views

Ito process with white noise

I would like to solve following system of SDEs, dx_i[t] = f[x_i[t]]*dt + dw_i[t] where d denotes ...
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0answers
41 views

Help!!! DSolve is coming out weirdly [closed]

The equation I am entering is 𝑥2𝑦′′ +𝑥𝑦′ +𝑦=4ln(𝑥) and it looks like DSolve[x^2 y''[x] + xy'[x] + y[x] == Exp[4 Log (x)], y[x], x] , it comes out as ...
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31 views

Trouble with bifurcation of differential equation

The code for bifurcation is written in such a way that it will allow plot bifurcation for any number of differential equation. Thus I am trying to avoid maps and iterations. Unfortunately it does ...
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2answers
144 views

Differential Equation in Complex Plane

I asked this question 8 years ago, but the answer of @Jens was not satisfactory and it didn't reproduce the plot exactly. I'm wondering if new versions of Mathematica can handle it.
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1answer
70 views

Translating the $\frac{u_x}{x}+\frac{u_y}{y}+\frac{u_z}{z}=\frac{u}{1-u}\quad u(\sqrt{y^2+z^2},y,z)=g(y)$ PDE into Mathematica notation?

This may be silly, but I am trying to find solutions to the following differential equation: $$\frac{u_x}{x}+\frac{u_y}{y}+\frac{u_z}{z}=\frac{u}{1-u}\hspace{2cm} u(\sqrt{y^2+z^2},y,z)=g(y)$$ On ...
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1answer
114 views

How to substitute a random function into a solution of a differential equation?

I would like to solve a differential equation including a source term. The source term is a random variable and I model this by creating a list of RandomReal and ...
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2answers
59 views

Unable to plot a solution of NDSolve whilst being able to evaluate it

I want to define a function $f_c(x,y)$ as the solution of the PDE $\Delta f_c(x,y) = g_c(x,y)$, where $g_c$ is a given function depending on a constant $c$. I tried the following: ...
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2answers
263 views

How to solve this PDE

I had a try at numerically solving the heat equation with a source term: $$ \frac{{\partial x}}{{\partial t}} = D\frac{{{\partial ^2}x}}{{\partial {z^2}}} + c $$ ...
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2answers
81 views

3D plot of the spatial path of velocity/space stochastic differential equations

I define the following 6 dimensional stochastic (Ito) process- in velocity v/position x. I can plot x1 as a function of t- see script below which has been corrected by Daniel. My goal is however to ...
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0answers
50 views

Solving a 1D diffusion equation [duplicate]

I am new to Mathematica and I'm trying to find the analytical solution to the diffusion of excess pore pressure in a porous media using this equation: $$ \frac{\partial P}{\partial t} - \alpha \nabla^...
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0answers
37 views

Set the arbitrary coefficients to zero after obtaining a solution form DSolve [closed]

After solving an ODE with 'Solve' function, I'm getting a result as Now I know that the coefficients $c_1, c_2$ have to be zero when I impose further restrictions on the solution, so after obtaining ...
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2answers
67 views

how to animate a 2D plot evolution from the 3D plot (solved using NDSolve)?

I have the problem of trying to get 2D plot from a 3D plot (which used NDSolve to solve the PDE), and I need the 3D plot's x-axis and y-axis to be the axes for my 2D plot while the z-axis of it to be ...

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