Questions tagged [differential-equations]
Questions on the symbolic (DSolve, DifferentialRoot) and numerical (NDSolve) solutions of differential equations in Mathematica.
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In Plot, different x range shows different result. Is it a bug? [duplicate]
After ODE, plot within {t,0,50} and plot within {t,0,60} have quite different results at some time instants.
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Bifurcation and stability analyses of delay differential equations
Are there any packages in Mathematica for bifurcation and stability analyses of delay differential equations? For Matlab, there is a nice tool like:
https://twr.cs.kuleuven.be/research/software/delay/...
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Mathematica gives weird solution to $y=xy'+y'$ [closed]
So I am practicing solving differential equations using Mathematica, and I will usually get an answer that I can easily verify. (as in I solve the differential equations myself and then check with ...
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NDSolve ignores my NeumannValue boundary conditions
I am trying to solve a simple linear differential equation for $f(x,y)$ on a square with area $L\times L =1$.
I consider
$(\partial_x^2 + \partial_y^2)f + \partial_x \partial_y f = 0$ with the ...
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Numerically solving radial Schrödinger equation with Yukawa potential
I am trying to solve the radial Schrödinger equation using NDEigensystem but I am running into some issues. There are posts about doing this (see here for example), ...
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Solving PDE for Diffusion Equation with Both Ideal and Excess Potential (Boundary Condition Issue)
I am trying to solve this partial diffusion equation shown
$$\dfrac{\partial C_A}{\partial t}=D_A\left[\dfrac{\partial^2C_A}{\partial r^2}+\dfrac2r\dfrac{\partial C_A}{\partial r}+\dfrac1{K_BT}\dfrac1{...
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How the function NDSolve works? [closed]
I am trying to numerically solve a system of ordinary differential equations.
...
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DSolve returns "Inverse functions are being used by solve; so some solutions may not be found", but it seems it returns all results
Sometimes, DSolve would return
Inverse functions are being used by Solve, so some solutions may not be found
but it seems it has returned all results. For example,...
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ParametricNDSolve doesn't correctly parse black-box function involving both independent variable and parameter
Consider this toy example:
f[t_?NumericQ, a_?NumericQ] := t + a
tst = ParametricNDSolveValue[{x'[t] == f[t, a], x[0] == 0}, x, {t, 0, 1}, {a}]
...
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Convert MATLAB code solving 1D wave equation via FFT using ode45 into Mathematica code
I don't quite understand the process of solving differential equations by MATLAB. It seems that it doesn't need the explicit function to specify the required solution, but only needs to input the ...
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Manual updating of function in Do loop
Previously I had asked a question about solving Maxwells equations with boundary conditions, here Machine overflow when defining boundary conditions.
I have managed to successfully run the code ...
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Fitting delay differential equations (DDE)
I have the following differential equations:
$$S'(t) = 0.31 S(t) \Big( 1 - \frac{S(t)}{6.19} \Big)- \frac{a}{1 + B(t)} S(t),$$
$$B'(t) = c (1 - B(t)) - d B(t) S(t) - 3 c (1 - B(t - 18)),$$
where $B(t -...
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Why is the result of "D[y == Log[x*y], x]" "0 == 1/x"? [closed]
In Mathematica 13.3.1, the D[y == Log[x*y], x] gives result 0 == 1/x. It is very weird. At WolframAlpha, its result is ...
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Chi-square minimization error
I'm trying to fit some data into a model using the standard procedure of minimizing the chi-square function using this code:
...
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Method of lines - Dirichlet and mixed BC
I have a dissolution problem to solve with two equations (everything is in dimensionless form - concentration, time and distance - EDIT: that came from the second Fick's law, where the distance was ...
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Unable to improve accuracy of MethodOfLines
I'm studying a PDE which roughly models a rope subjected to driving on one end. The coordinate $v$ is related to physical time $t$ via the relation $v=t-x$. I'd like to solve the initial value problem ...
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Badly conditioned matrix for boundary ODE
I have a coupled boundary ODE with dependent variables $u=u(x)$ and $z=z(x)$,
$$u'' - \frac{1}{z} \left( -3 + u'^2 (3 - c\; e^{-g u} z^4) - 6 u' z' \right) = 0\tag{1}$$
$$z'' + c\; e^{-g u} z^3 (-3 + ...
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Solving the integral equation
Why does Wolfram Mathematica just rewrite my code instead of solving the integral equation? SigmaPhiBegin, SigmaPhiEnd are functions depending on Rho, Rho, bEnd, a, Kappa are constants. What needs to ...
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Taylor approximation of integrals
I have BVP as in the picture and I want to solve it numerically by method given as follow. In the original paper, it is motioned that first iteration is computed and other are computed with Taylor ...
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Using Reduce to simplify (not solve) system of equations
I'm dealing with a Mathematica program that generates a set of coupled non-linear equations involving an unknown function and its derivatives with respect to at least one independent variable. My goal ...
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Normalized Coincident Detection Probability of Laguerre - Gaussian Modes
I am working on a paper in which a pump mode is passing through SPDC(Spontaneous Parametric Down conversion) is converted into two photons called as signal and idler. In which laguerre-Gaussian mode ...
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Extract boundary points of an interpolating function obtained by NDSolve
Given a set of coupled nonlinear equations I want to extract the boundary points that appears in the interpolation function obtained as an output to NDSolve function and then to define them directly ...
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Which condition is better for WhenEvent?
I'm solving a non-linear system with NDSolve. See my previous post
In the WhenEvent, which one is better for ODE solving
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Trouble implementing switching hybrid system with NDSolve
I'm trying to use NDSolve to simulate a hybrid nonlinear system that switches between different linear behaviors based on states and inputs (i.e. switching from one linear behavior to another) which ...
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How to include impulses in differential equations?
I have two coupled differential equations as follows:
$$S'(t) = - \frac{a}{1 + B(t)} S(t),$$
$$B'(t) = \frac{c}{1 + S(t)} B(t) (1 - B(t)) - d B^2(t) \Big( \frac{1 - B(t)}{B(t)} \Big)^n,$$
where $a$, $...
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Error in using the function NDSolve [closed]
I am trying to numerically solve a system of ordinary differential equations.
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Is there a way to improve the speed of the NDSolve in my code?
I want to tell the background before raising the question of details.
My boss and I are designing synthersizer in a millimeter-wave chip. He analyzes the transient behavior with Julia. His code is ...
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Using ParametricNDSolveValue and MultiNonlinearModelFit to fit an ODE system to datasets
I asked a question here about fitting an ODE system to given datasets. The great answer of @ydd solved the problem nicely. In the mentioned answer, the initial values are taken as the initial points ...
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NDSolve fails to solve trivial PDE with mixed partial derivatives
Consider the following PDE with independent variables $(x,t) \in [0,1]\times[0,\infty)$
$$2u_{xt}(x,t)=u_{xx}(x,t)$$
initial condition $u(x,0)=1$ and with boundary conditions $u_x(0,t)=0$ and $u(1,t) =...
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Modeling experimental data with differential equations
I have the following two sets of experimental data, which show the dependencies of two quantities, namely, $S$ and $B$, on time ($0$ h, $3$ h, $6$ h, $9$ h, $15$ h, $18$ h, $21$ h, and $24$ h):
...
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xAct/xCoba and DSolve Don't Work Together
Context
I'm trying to derive the Reissner-Nordstrom metric for a charged nonrotating black hole using xAct. The idea is to first have a metric of form
$$ds^2 = e^{2\alpha(r)}dt^2-e^{2\beta(r)}dr^2-r^...
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DSolve doesn't produce the expected result
I have the following function:
$$B(t) = \frac{a^n}{a^n + t^n}.$$
By taking derivative from both sides with respect to $t$ and after some manipulation, one obtains:
$$B' = - \frac{n}{a} B^2 \left(\frac{...
user95418
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Optimizing an ODE fitting algorithm with interpolated data
Given data, I want to find parameters $p_1,p_2,k_1,k_2>0$ that fit the following ODE system
$$
\begin{align}
b'(t)&=p_1 a(t)-k_1b(t)\\
c'(t)&=p_2b(t)-k_2c(t)
\end{align}
$$
where $a(t)$ is ...
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How to solve the following integrodifferential equation by generic approach?
Consider the following equation:
$$
\frac{\partial f}{\partial t} - p H(t)\frac{\partial f}{\partial p} = \mathcal{I}[p,t], \tag 1
$$
Here, f = f[p,t], with p being ...
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Calculating the largest Lyapunov exponent with NDSolve for a damped pendulum
I'm using Mathematica to compute the maximum Lyapunov exponent for a damped pendulum. Ideally, when the damping is zero, the exponent should be zero, and for finite damping, it should be negative. ...
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NDSolve producing oscillatory results
NDSolve producing very oscillatory solutions even after not having any large numbers or warning/errors
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Solving PDE for Diffusion Equation (Boundary Condition Issue) [duplicate]
I am trying to solve this partial diffusion equation shown
$$\dfrac{\partial\overset\sim\rho_c}{\partial\overset\sim t}=D_c(\overset\sim r)A\left(\dfrac{\partial^2\overset\sim\rho_c}{\partial\overset\...
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Numerical instability due to convection dominated PDE [duplicate]
I am trying to solve this partial diffusion equation$$\dfrac{\partial\overset\sim\rho_c}{\partial\overset\sim t}=D_c(\overset\sim r)A\left(\dfrac{\partial^2\overset\sim\rho_c}{\partial\overset\sim r^2}...
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Imaginary Result on NDSolve+NIntegrate
I posted the same question in the Physics StackExchange, wondering if it is physics problem. I haven't received any answers, so I am posting in Mathematica StackExchange to see if it is programming ...
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Numerical solving diffusion equation in spherical coordinates
Mathematica nicely solves Poisson's equation in spherical coordinates as
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First order differential equation with two conditions
I want to produce all possible solutions for this equation:
...
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How to fit a linear ODE system?
Consider the equations
$$
\begin{align}
b'(t)=p_1 c(t)-k_1b(t),\\
c'(t)=p_2b(t)-k_2c(t)
\end{align}
$$
Given data on $b$ and $c$, and initial conditions, how do I find the best fitting parameters $k_1,...
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Step problem in NDSolve with FixedStep method
We want to solve a set of ODEs with fixed step, whose size is 1/1000, the related codes are given in the following.
The parameters are given by
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Trying to plot the Fourier transform solution to the heat equation on Mathematica [closed]
I have gotten the solution of the heat equation as
where f(y) is the initial heat distribution which I have been given as f(x) = e^([Sigma]x^2).
I am supposed to plot this at the value of sigma 1, 2 ...
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