# Questions tagged [differential-equations]

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

1,063 questions with no upvoted or accepted answers
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154 views

### Fluid Flow PDE with Mass Conservation

Modeling a simple stepped nozzle for gas flow and having difficulties with the application of the mass conservation equation as part of the boundary conditions. I am following the fluid flow example ...
113 views

### NDSolve can solve two systems of equations separately but not simultaneously

I want to solve a system of coupled equations. After facing problems solving the coupled system, I reduced it to both of the systems uncoupled. Even uncoupled, the equations will not solve ...
190 views

### Boundary value problem, multiple dimensional shooting, coupled eigenvalue problem

Following the one dimensional boundary value problem here, I would like to understand the easiest way to solve a BVP for a coupled system. In the 1D case, BVP can be converted to an initial value ...
956 views

### how to obtain general solution for Laplace PDE in spherical coordinates using DSolve?

Can DSolve given a general solution to Laplace PDE in spherical coordinates without given boundary conditions? I tried, but not able to get a solution. Do I need ...
215 views

### Where to find LieSymm-PDE Package for Mathematica?

I am unable to find the LieSymm-PDE package for Mathematica developed by Vladimir Pulov et al as outlined on the website: http://www.swmath.org/software/12188 as well as explained in the paper: https:/...
459 views

### Wormhole embedding diagram

I am trying to reproduce the embedding diagrams for the evolution of a Schwarzschild wormhole described in this paper. Following the paper notation, we denote the Kruskal coordinates by $(v,u)$. For ...
446 views

### Automatic Boundary conditions in NDSolve

I would like to know what kind of boundary conditions Mathematica implements in NDSolve when not specifying any boundary conditions by hand. So for example solving ...
357 views

### NDSolve Problem with step size and Stiffnes

I need to solve a 5 coupled non-linear differential equation system. There seems to be no apparent singularity but whenever I tried to evaluate the system in Mathematica. It gives the error ...
71 views

### How to check that a function is solution of an ODE with Mathematica

Let $$S(t)=\int_0^t\int_t^\infty \left(\frac{1}{(1+x^2)^{1/4}(y-x)^{\frac{3}{2}}}-\frac{1}{(1+y^2)^{\frac{1}{4}}(y-x)^\frac{3}{2}}\right)\mathrm d y\mathrm d x.$$ Is there a way to check with ...
77 views

### Confused on the Positionvariables in SymplecticPartitionedRungeKutta Method for NDSolve

I am solving a set of differential equations with symplecticpartitioned runge kutta method. After checking my code for a long time, I found the example code in the tutorial of Mathematica also has a ...
264 views

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### Improving the speed on an iterated differential system

I'm working on a simulation where I need to solve a differential system for a function, and then use the solution to this system to calculate another function that is used as an input to this ...
769 views

### Linear tangent steering law and orbital insertion altitude

I've been trying to figure out how to build a rocket launch simulation that allows the user to specify the desired altitude at which a payload will be inserted into a stable circular orbit, but have ...
216 views

### Modelling heat exchange between flowing fluid and surroundings

Starting from this question: Couple a PDE and ODE in NDSolve I would like to modify the fluid from static to a flowing one in the y direction. that's the original code that I modified a little bit: ...
66 views

### How to fix a problem like this in NDSolve?

I am a beginner on Mathematica. Now I am trying to solve second-order PDEs using NDSolve. But I encountered the following error. Could anyone help me find out the mistake I made? Thank you in ...
264 views

### Solving Differential Equation for derivative

I am new to mathematica and am trying to solve a differential equation. Actually, I am not entirely sure if the system can be called differential equation. I am interested in finding out the second ...
249 views

### NDSolve with only discrete variables

Is is possible to use NDSolve with DiscreteVariables if there are no continuous-time variables? This fails: ...
223 views

### How to change the boundary condition near singularity

The following system has a singularity around $x=0.451$. What I want to do is to detect when the solution gets close enough to this singular point (in this example I'm using the threshold of $0.001$), ...
96 views

### NDSolve problem in Mathematica 10.1, possible bug

The following code, ...
150 views

### Unusual error message from Solve when called by DSolve

Question 111150 presents an equation nonlinear in its leading derivative ...
85 views

### wrong sign with NeumannValue

I want to use NDSolveValue with Neumann boundary condition. The documentation says this https://reference.wolfram.com/language/ref/NeumannValue.html . In the ...
158 views

### NDeigensystem returns error due to mesh discretization when calculating vibrations of a cantilever

There was an transcription error in the code I provided in a previous post: https://mathematica.stackexchange.com/questions/105713/ndeigensystem-returns-complex-non-hermitian-error-for-the-...