# Questions tagged [differential-equations]

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

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### PDE with Excess Potential

I am trying to solve this PDE with excess potential and the code is shown below. ...
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### How to solve solve an ODE that depends on a strictly positive parameter?

To solve the ODE f'' + f = 0 on (0, 1) f(0) = f'(1) = 0. I use the command ...
1 vote
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I have: ...
1 vote
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### FindRoot + NDSolve + List? [duplicate]

I've noticed that FindRoot fails when its argument involves a component of a list, to which a substitution rule from NDSolve has ...
38 views

### 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. ...
1 vote
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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/...
1 vote
115 views

### 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 ...
118 views

### 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 ...
900 views

### 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), ...
48 views

### ParametricNDSolveValue as replacement rule [closed]

I have a system of 4 non linear differential equations x[t],y[t],z[t],w[t]with one free parameter a solved with ...
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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 ...
143 views

### 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 ...
1 vote
103 views

### 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 ...
1 vote
105 views

### 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 ...
1 vote
65 views

### 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 ...
1 vote
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### Discrete number does not work well in DSolve

The code below works fine. ...
74 views

### 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 ...
37 views

### 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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### 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): ...
77 views

### I want to know why my DSolve don't show any result

Why is DSolve not showing a result in the following code of mine? ...
70 views

244 views

### 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 ...
214 views

### 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 ...
56 views

### Calculating the largest Lyapunov exponent with NDSolve

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. ...
1 vote
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\...