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Questions tagged [differential-equations]

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

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Differential equations system's solutions differ when one of the constant is 0

I am solving the following system of equations with Mathematica. $u'=-k_{1}ux+k_{2}x^2, x'=k_{1}ux-k_{2}x^2$ and I obtain the solution for x: $x(t)=\frac{e^{k_{1}C_{1}(t+C_{2})}k_{1}C_{1}}{-1+e^{k_{1}...
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23 views

How to `DSolve` this differential equation?

How can I DSolve this equation? ...
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10 views

Problem in implementing periodic boundary condition to solve a system of PDEs with period 2 Pi/constant

I wish to solve the following system of PDEs for h1, h2 using periodic boundary conditions and specified initial conditions. When I execute Mathematica complains that the boundary conditions are not ...
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34 views

3 body problem for earth sun and moon

Im trying to model a 3 body system consisting of the sun, earth and moon. ...
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15 views

System of delay differential equations: using first interpolation as second initial condition

I am trying to solve numerically the following system of two coupled delay differential equations: $$\dot x(t)=-\gamma x(t)-\frac{\gamma}{4}e^{i\omega_0\tau_1}y(t-\tau_1)\theta(t-\tau_1)+\frac{\...
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Is Mathematica calculating Lagrangian correctly?

The following Lagrangian is available: $$ L = (\omega(t))^2J(t,\theta(t))-m(\omega(t))G_gP(t,\theta(t)) $$ Here $\omega(t)$ is the angular velocity of the body; $J(t,\theta(t))$ - a variable moment of ...
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27 views

Implementing a generic product rule

I'd like to implement a generic rule for expanding differential forms by the product rule. For instance, I'd like to transform the following PDE: $\phi \frac{\partial \phi}{\partial t} = \phi \nabla^...
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71 views

How to extract some specific value from NDSolve?

How can i extract some value from NDSolve. We know that gives us a InterpolatingFunction. But i need to use some specific value. For example this is the NDSolve: This is the equation used ...
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22 views

Need help with the “step size is effectively zero; singularity or stiff system suspected” message

I'm trying to solve a system of ODEa, and I always get a message saying NDSolve::ndsz: ..step size is effectively zero; singularity or stiff system suspected. I tried ...
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37 views

Speeding up the process of NDSolve[] when a user-defined function is involved?

I am trying to tackle a (1+4 dimensional PDE) model at which the solution of the first PDE (with some interpolations and changing the domain) would be used in the second PDE. In fact, I must choose ...
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101 views

Non-linear differential equation with tricky variable dependence

My problem regards solving a differential equation and can be reduced to the problem of finding $f(x)$ such that $\frac{df}{dx}=\frac{dh}{df}$, with $h(f)$ a known function. I have this list of data,...
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Where is the numerical solving breaking down?

I am working with a set of three coupled reaction-diffusion PDEs, and for some parameter values I am getting some not so great solutions. I have been searching documentation and tutorials, and I have ...
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1answer
39 views

Does NonlinearStateSpaceModel work with symbolic constants?

I'm trying to put a nonlinear system of two 2nd order ODEs given by: ...
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1answer
56 views

Trying to use NDSolve to solve a system of non-linear PDEs representing the development of Alzheimer's disease over time

I'm trying to do something very similar to this question, except with a much larger system of PDEs from this paper. The PDEs are equations 1-18 in that paper. Equations 9, 10 and 15-18 have laplacian ...
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1answer
61 views

Numerically solving a system of ODEs with parameters [on hold]

I am working on solving a system of coupled ordinary differential equations with initial values given. When I searched about my requirements I got the similar answer here. But I got another condition ...
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41 views

NDSolveValue::fembdcc: Cross-coupling of dependent variables is not supported in this version

It seems that Mathematica can't solve differential equation when one of the arguments requires that the value of one variable is equal to the value of the other variable, when I try this I get this ...
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2answers
51 views

Error in a simple plotting code [closed]

I have the following code: ...
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31 views

NDSolve::conarg: The arguments should be ordered consistently mistake [closed]

I want to solve a system of differential equations, but I get NDSolve::conarg: The arguments should be ordered consistently mistake. How can I avoid that? code: ...
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30 views

How to convert this equation to a second order one in f?

This is a third-order differential equation. Is it possible to convert it to a second-order one by integrating it or any other way? I think it could be done by multiplying by some additional factors. ...
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1answer
114 views

Solving the Stokes equation for planar Marangoni flow with FEM

Background I would like to numerically solve the stationary Stokes equation from fluid dynamics $\eta_i \nabla^2 \vec{u}_i - \nabla p = 0$ with the incompressibility condition $\nabla \cdot \vec{u}...
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1answer
59 views

Solution of a system of ODE with Dsolve

I am trying to solve following ODE with Dsolve. a1[t_] = 2 - 3*Exp[-2*t]; a2[t_] = 1 + Exp[-3*t]; a3[t_] = 4 + Exp[-5*t] $B=\begin{bmatrix}a1[t] & a2[t] &...
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43 views

Plot a solution of two parametric fuctions [closed]

Please I need Help, I have the following system of linear differential equations ...
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1answer
59 views

How to substitute by NDSolve solution to plot a new function

Assume I got some function by NDSolve , like y(t) ...
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62 views

How to solve this equation in Mathematica?

I wonder what is the best way to solve this equation in MA? $$ y= \frac{\partial}{\partial x} ~ \frac{\partial}{\partial x^*} f $$ where y and ...
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95 views

Function value errors in NDSolveValue

I am solving a second order differential equation described by odey below. For the asymptotics, I have the following code which will be used as initial conditions for NDSolve. ...
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1answer
66 views

Polar plotting Hankel Function with a lot of terms

I am trying to plot a normalized polar plot for the following function with different values of $a$ $$\left\lvert \sum_{n=1}^\infty i^n (2n+1) \frac {P_n^1(cos(\theta))}{\sqrt{\frac{\pi k a}{2}}[-H_{...
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1answer
144 views

How can I get the Green's function of a certain differential equation?

Ho w to extract the green function of the following differential equation. I am trying to extract the analytical form of the green's function. \begin{align*} EI_{zz}\,\frac{\partial ^2u\left(x\...
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1answer
80 views

Geodesics in 2+1 Schwarzschild metric

Would appreciate if someone could explain the query that, I am trying to understand the code for timelike geodesic in 2+1 Schwarzschild $(\theta=\frac{\pi}{2})$ where we have taken $M=1$. From this ...
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1answer
24 views

Error when trying to solve a linear differential equation

I am trying to solve a linear differential equation for the change in scale factor term, $\delta a(t)$, when mass terms are introduced to the equations of motion for General Relativity. The first ...
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29 views

How can I use WhenEvent to stop the integration? [duplicate]

I have a questions about stopping the integration. I calculate the function as the following. It gives the message: "At NN=58.7035438......, the step size is effectively zero; singularity or stiff ...
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1answer
76 views

Solving these equations with a constraint

I have been for long time now try to solve this equation q1[t_] = D[x[t], t, t] - 2 (1/y[t]) D[y[t], t] D[x[t], t] With its complex conjugate ...
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1answer
54 views

Can Mathematica check ansatz for solutions of differential equations?

I'm just a beginner learning Mathematica. I'd like to do something with it, but I don't know if it is possible. Suppose I want to solve a system of differential equations, maybe a nonlinear one, and ...
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2answers
82 views

Need more equations in PDEs by NDSolve? Bug of mma?

I am trying to solve set of pdes as below ...
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57 views

How I can plot Vector3DPlot?

I want to reproduce the vector 3D plots as shown in the figure. It's in spherical polar coordinates (i.e. vector 3D plot on plane). The angle [Theta] is spherical coordinate is determined by the ...
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41 views

NDsolve set of pdes with minus power

I am trying to solve set of pdes as below ...
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56 views

Fail to solve set of PDEs

I tried to solve a[t,z] and u[t,z] from set of PDES. Here a[t,z] describes laser incident on ...
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47 views

Performance Optimizing ParametricFunction

Setting up the system: ...
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1answer
63 views

Laplace equation DirichletCondition ignored

My goal is to find out force between two parallel identical disks with Voltage difference. To solve this, I tried to use laplace equation. And below is my code. where R is radius of disks, d is ...
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55 views

how to solve nonlinear differential equations which calls other functions that uses states and time as input while solving NDSolve?

I have nonlinear differential equations which require output from other functions and those functions require time and some states as input. I'm writing the Mathematica code bellow the equation. $p=...
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53 views

RK4 of second order ODEs system

I'm new here and I have to program explicitly a Runge-Kutta 4 Method for a second order ODEs $10 \times 10$ system: $X''(t)=AX(t)+F(t)$, and the instruction was to make a change of variable $y(t)=x'(t)...
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72 views

Why Mathematica gives this second solution to this first order linear PDE $w_t+3 t w_x=w$?

This is using V12 on windows 10. I was trying to verify my hand solution with Mathematica. DSolve gives two solutions instead of one, which I do not understand ...
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1answer
83 views

Bifurcation diagram for ODEs

I have a system of ODEs ...
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2answers
53 views

How can I solve this differential equation?

I have a differential equation and when I try to solve it by using the "NDSolve" command, the Mathematica gives an error. The differential equation and error are as follows ...
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55 views

Simplifying a differential equation acting on a product of functions

I have a function $f(x_1, \ldots , x_n)$ in $n$-variables that satisfies a fourth order linear differential equation (say $Df=0$). The function $f(x_1, \ldots, x_n)$ is of the form $f(x_1, \ldots, x_n)...
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34 views

Adding extra species in a model

I am currently working on a model of competition for resources between different species. I have 6 species competing for 3 resources. The first 3 species start at =0. the 4th species is added at t=...
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1answer
69 views

How to chop a complex number?

I'm solving some differential equations by iterating and I want to use Chop to get rid of noice smaller than a certain threshold. However, I found that Chop only "chops" the real part, not the ...
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41 views

How to solve forward Kolmogorov birth-death equations for unspecified number of populations

I'm attempting to use a forward Kolmogorov differential equation to model a birth-death process. This is fairly trivial when there's only one population, but I'm working with an unspecified and time-...
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40 views

How to resolve underflow occurrences?

I am solving a second order differential equation described by odey below. For the asymptotics, I have the following code which will be used as initial conditions for NDSolve. ...
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0answers
41 views

Non-linear ODE from closed-loop system and Response (Part II)

I again need help with the Mathematica. We have the following affine system. I need to get expressions describing the changes of $x_{1} \left( t \right)$ or $x_{2} \left( t \right)$. The only thing ...
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1answer
39 views

How to create a correct density plot from “NDSolve” solution?

I would like to create the projection of a solution in plane from the differential equation set solution. However, the way I did it is not as I would like it, it does not have a smoothness. Here's ...