# Tagged Questions

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

216 views

### How can I solve a 3D heat transfer partial differential equation? [closed]

It's a problem about heat transfer. Here is the equation : Is it solvable using this software? Edit Sorry, I'm new to Mathematica. I have the following code for this problem ...
62 views

### NDSolve::bcedge error when solving PDE on a square region

I am solving a 2D PDE system: ...
104 views

### FindRoot of interpolating function from NDSolve

I am having issues finding the root of an interpolating function obtained from NDSolve. For example: ...
72 views

### How to select coefficient of an exponential function

Suppose I have these set of equations: sol = DSolve[{ x'[t] == -RandomReal[]*x[t] + y[t], y'[t] == x[t] - *y[t] , x[0] == 1, y[0] == 0}, {x[t], y[t]}, t] The ...
102 views

### Numerically Solving Helmholtz over the Rectangle - Why does this code only give eigenfunctions of the form $u_{m1}$ [closed]

I have been following the method for numerically solving the Helmholtz equation in this example (the answer by User21) and have come across two problems. I have been implementing the method for a 2x1 ...
133 views

### Solving quantum harmonic oscillator in 1D for a displacement of the ground state as initial state [NDSolve]

As an exercise, I want to numerically solve the quantum harmonic oscillator in 1D. ...
163 views

### NDEigensystem producing imaginary eigenfrequencies for the vibrations of a cantilever [closed]

We are trying to use NDEigensystem to solve for the vibrational modes of a cantilever with triangular cross-section. However, many of the solutions provided by NDEigensystem have imaginary ...
69 views

### Assigning multiple solutions different replacement names

Let's say we are solving a homogeneous differential equation, such as $$y^{\prime\prime} + a y^{\prime} + b y = 0$$ with characteristic equation $$s^2 + a s+ b = 0.$$ Using the ...
175 views

### Trying to simulate pulse width modulation

I am trying to simulate a pulse width modulated signal in a NDSolve, but i have a hard time passing the signal function in. This is my code: ...
182 views

### Bug? Problem with derivative of interpolating function from FEM

Bug introduced in 10 or earlier and fixed in version 10.4 I am really not sure if this is a bug or I am missing something very trivial. QUESTION: What I am missing in order to obtain the partial ...
73 views

### How to plot dy/dx and y together for a differential equation? [duplicate]

For the differential equation y'(x)+a*y(x)=d, how to plot y'(x) and y(x) for given values ...
48 views

### Problem in trying to solve a differential equation [closed]

I'm trying to solve a differential equation but not getting a solution. Some references I read gave me hits about using a runge kutta method. I'm new to the software, any hints regarding this error ...
64 views

### Help numerically solve this non-linear PDE with singularity

I have trouble finding a numerical solution to the partial differential equation below. It seems to be a singularity in the solution somewhere, so I searched online and found that it is suggested to ...
191 views

### Can I get rid of the noise in my differential equation solution?

I am solving a differential equation: ...
77 views

### Differential equations expressed in operator form [duplicate]

Is it possible to make a workable operator representation of differential equations in Mathematica? I think it would make solving my differential equations easier, but I have no idea how to do it. ...
422 views

### Problems when solving a nonlinear PDE system with NDSolve

The nonlinear PDE system is actually extracted from a research paper published in 2000 Here is the paper link The authors solved the system by using an ordinary differential equation integrator in ...
72 views

### Paramter Scans and $\chi^2$ Test in Mathematica

Is there any in-built function or a recommended package that enables one to find, say, 10 Parameters, which are used as boundary conditions in NDSolve, that minimize $\chi^2$? ...
99 views

### Bessel-like equation problem with NDSolve

I am trying to solve the following nonlinear ODE, but Mathematica takes forever to give a result. Any idea why? ...
44 views

### Differential equation for a list with parameter dependent function

I am having a differential equation: y' = (1 - y) - f[y, mu] y; f is a hysteretic function that depends on y and on the derivative of y: ...
37 views

### Recursions where one definition depends on another. How to Block or have local variables?

I have been using Mathematica to solve a second order differential equation using the second order Verlet method. My code looks like: ...
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### How to enforce a symmetric solution with FEM?

I'm solving the laplace equation in a domain with holes, and I need to compute the integral of the gradient on the boundary of these holes. For that I define a mesh and solve the laplace equation ...
34 views

### Replace variable with other variable containing a constant in differential expression [duplicate]

I have the following differential expression: ...
111 views

### Integration of Frenet-Serret differential equations [duplicate]

Are there programs available in Mathematica or other related sources where third order Frenet-Serret equations are numerically integrated to find coordinates in 3-space? Curvature/torsion given as ...
44 views

### implicit solution to PDE with strange return type

I want to solve the following PDE eqn = D[q[k, t], t] + \[Alpha] (1 - q[k, t]) D[q[k, t], k] == q[k, t] (q[k, t]-1) for $q(k,t)$. The solution that is returned ...
111 views

### Finite Difference - heat generation in a square (square within a square)

I am trying to develop a code that will allow me to solve the following problem. Lets say that I have a square block, inside that square block I have a smaller square box thats at a certain ...
167 views

### Differential equation in two variables

I have a system of second order differential equations, with two independent variables, which represents a trajectory. I tried solving this system using NDSolve and ...
I have an equation $$\bigl(r''(\phi)r(\phi) - r'(\phi)^2\bigr)\bigl(b + r(\phi)\bigr) = r(\phi)\bigl(r'(\phi)^2 + r(\phi)^2\bigr)$$ Here $b$ and $r$ are lengths, and $\phi$ is an angle (in radians, so ...