# Questions tagged [differential-equations]

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

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66 views

### How to change the default normalization for NDEigensystem?

I'm currently using NDEigensystem to solve a PDE that describes a particle travelling on a hyperbolic (negatively curved) surface. However, the eigenfunctions that are returned by NDEigensystem are ...
67 views

### Laplace equation for cylindrical rods

I have a system of four cylindrical rods with a certain radius, length, and separation. I have applied different voltages to the rods. I want to solve the Laplace equation, but I am unable to give ...
74 views

### Why unable to verify solution to first order PDE?

This is using V12 on windows. I solved this PDE by hand and wanted to ask Mathematica to verify my solution. But Mathematica solution does not look like mine. And when I tried to verify Mathematica ...
59 views

### DSolve Doesn't Return a Solution or Error

DSolve is not returning anything other than the original expression on ...
40 views

### How to solve integral equation involving Fourier Series

I have a set of equations involving two anti periodic functions $f(t+T)=-f(t)$ and $g(t+T)=-g(t)$ \begin{cases} f(t)&=J^2g(t)^3 \\ \mathcal{F}[g](\omega_n)&=\frac{1}{-i\omega_n-\mathcal{F}[...
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### How to increase the integration domain of NDEigensystem without a “non-Hermitian” error?

Recently, I've been using NDEigensystem to solve a two-dimensional eigenfunction equation. The region that I'm solving over is as follows. ...
55 views

### Take limit in NDSolve

I have this equation : eqkk = D[k[t], {t,2}] - ((3 sola'[t]/sola[t]) + (3 sola''[t]/sola'[t]) - (1/(sola'[t] sola[t]^2))) D[k[t], t] To get $k(t)$: <...
96 views

### Poincaré sections for oscillating system

I need to build Poincare maps for solutions of a system of differential equations. This system includes the mass of an oscillating particle. If the mass value is made very small (m ~ 10 ^ -25) the ...
50 views

### Could not able to set up a differential equations using EulerEquations command

I have a constructed the Lagrangian of a mechanical system by finding the kinetic and potential energy of the system. Then I tried using EulerEquations to set up a differential equation by taking the ...
90 views

### Using multiple boundary conditions with NDEigensystem

I'm quite new to Mathematica and to Stack Exchange so I apologise if this question has already been answered. I've recently been trying to solve a partial differential equation to find the ...
32 views

### DSolve not giving a solution

I tried solving this but no result, I tried eliminating the initial condition, replace the zeroes in boundary condition but nothing is working. Thank you in advance
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### How to keep the numerical integration when an event occurs?

I'm numerically integrating the following system, f[r_] = 0.904965 - (1 + 12.7028/r^2) (1 - 2/r) dϕdλ = 1/r[λ]^2; eqc = r'[λ] == Sqrt[f[r[λ]]/(dϕdλ^2)]; with the ...
62 views

### Stiffness and NDSolve error NDSolve::ndsz:

I have a 2nd Order ODE problem I am trying to solve numerically in Wolfram: $$(k^2-1+\frac{2x}{x^2+c^2})\frac{d^2y}{dx^2}+\frac{c^2-x^2}{c^2+x^2}\frac{dy}{dx}+x\frac{x^2-3c^2}{(x^2+c^2)^3}y=0$$ ...
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### Why doesn't Mathematica evaluate the series with recursion relationship as expected?

I define a series $dg(i)$ as the $i$th derivative of a function $g[t]$ for $i>0$ and known the first term $dg(1)=(t-x)g(t)$. In mathematica, the code is: ...
58 views

### Specify direction of propagation in the 1-d wave equation in NSolve and NDSolve [duplicate]

I am solving the 1-d wave equation with the following initial conditions: ...
36 views

### Defining a function through an ODE containing unspecified operators

I want to do some algebra using a function only defined through a DE containing unspecified operators. The DE is $$\partial_zu(z) = \left[\hat{D}+\hat{N}(z,u)\right] u(z).$$ Here $u$ lives in ...
92 views

### Using NDEigensystem to find 100 eigenvalues

I'm using "NDEigensystem" to calculate a Sturm-Liouville problem, for which the first 100 eigenvalues are needed. The code is like this: ...
67 views

### Plotting basins of attraction of magnetic pendulum in spherical coordinates

I am new in Mathematica, and this is the first time I coding. Following is the code solving differential equations of motions in spherical coordinates of magnetic pendulum and plotting basins of ...
45 views

### NDSolveValue::bcedge: Boundary condition is not specified on a single edge of the boundary of the computational domain

I'm solving a Schrödinger's Equation in 1d, where $\Omega$ is the domain, bcs the periodic boundary condition, init the initial condition. ...
128 views

### Problems in running the non-linear PDE system

I'm new to the mathematica and just try to solve an seemingly simply non-lineal coupled PDEs. It is about the diffusion-reaction kinetics in a pellet.The code seems workable, but keep running without ...
70 views

### Estimating parameters on system of differential equations

I am looking for some help estimating the parameters of a series of differential equations to assist fitting the experimental data I have collected. The Problem: The equations are based off of the ...