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Questions tagged [differential-equations]

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

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68 views

How to chop a complex number?

I'm solving some differential equations by iterating and I want to use Chop to get rid of noice smaller than a certain threshold. However, I found that Chop only "chops" the real part, not the ...
40 views

How to resolve underflow occurrences?

I am solving a second order differential equation described by odey below. For the asymptotics, I have the following code which will be used as initial conditions for NDSolve. ...
40 views

How to solve forward Kolmogorov birth-death equations for unspecified number of populations

I'm attempting to use a forward Kolmogorov differential equation to model a birth-death process. This is fairly trivial when there's only one population, but I'm working with an unspecified and time-...
534 views

NDSolve`FiniteDifferenceDerivative gives wrong result when the precision is not MachinePrecision

Bug introduced in 8 or earlier and persisting through 11.0.1, fixed in 11.3 or earlier. I want to get a pseudospectral differentiation matrix by ...
40 views

Non-linear ODE from closed-loop system and Response (Part II)

I again need help with the Mathematica. We have the following affine system. I need to get expressions describing the changes of $x_{1} \left( t \right)$ or $x_{2} \left( t \right)$. The only thing ...
39 views

How to create a correct density plot from “NDSolve” solution?

I would like to create the projection of a solution in plane from the differential equation set solution. However, the way I did it is not as I would like it, it does not have a smoothness. Here's ...
99 views

Numerical resolution of non-linear coupled ODEs

I have problem with my code in Mathematica. I have introduced the set of coupled non-linear ODES. This is the resolution part: ...
87 views

In a simple example I try to solve the heat equation using NDSolve and Method->"FiniteElement". I know that NDSolve gives ...
28 views

Solving differential equations and plotting the function against a parameter

I wrote the following code using the function NDSolveValue ...
48 views

How to solve this ODE by DSolve or NDSolve?

I try to solve this second order ODE to get k: $\frac { \partial }{\partial z} ~ \frac{ \partial } {\partial \bar{z}}~ k[z, \bar{z}] = 5$ Where z is complex coordinates, so to take the ...
46 views

Why the StreamPlot and NDsolve diverge about this vector field?

I frequently use Streamplot and NDSolve for representing vector fields and their trajectories. But for the first time these tools present different dynamics. How can I fix it? I am putting here the ...
48 views

Second order differential equation not getting solved using DSolve

I am trying to solve this second order differential equation $-\frac{k T}{q n(x)} \frac{d^2n(x)}{dx^2} + \frac{k T}{q (n(x))^2} (\frac{d n(x)}{dx})^2 = \frac{q}{\epsilon} (N_D(x) - n(x))$. So I want ...
27 views

Solving numerically a dissipative non-linear system of coupled ODEs [duplicate]

My problem is to integrate a set of couple non-linear and first order ODEs. They are Eqs. (45) -- (50) in the paper https://arxiv.org/pdf/1901.03380.pdf. This is the set of differential equations I ...
34 views

I have this system of equations: $- \ddot{z} + \frac{1}{g} \frac{\partial g}{\partial z} \dot{z}^2 + \frac{1}{g} \frac{\partial g}{\partial z^*} \dot{z} \dot{z}^*$ =0 , $- \ddot{z}^*+ \frac{1}{g^*} ... 2answers 54 views Checking NDEigensystem Results I'm looking to verify the output of a call to NDEigensystem. I'm doing this by plotting the operator acting on the Interpolating Function outputs versus the ... 2answers 4k views ndsz : step size is effectively zero; singularity or stiff system suspected This is the first time I ask a question. I have seen many solutions to this error and tried but they are not working. Here is the code. ... 1answer 450 views Meniscus outside of a cylinder - axisymmetric Young-Laplace equation in semi-infinite domain How to solve the axisymmetric Young-Laplace equation $$\frac{z'(r)}{r \sqrt{z'(r)^2+1}}+\frac{z''(r)}{\left(z'(r)^2+1\right)^{3/2}}=z(r)$$ with b.c.s $$z'(1)=-2$$$$z'(\infty)=0$$ where$z=Z/l_c$... 0answers 31 views Time optimization of motion using mathematica Let us say I have a double pendulum, with the torque equations and the initial and final poisition of the end point of the pendulum. I have constraints on the maximum and minimum values of torques. I ... 3answers 74 views The solution of only one equation being recorded, when all solutions should be recorded [duplicate] I have the following code ... 0answers 44 views Using FullSimplify to simply expressions involving differential operators I am trying to simplify some long formulas involving differential operators in$n$variables. For example, I want to simplify $$\left(\frac{\partial}{\partial x}-\frac{\partial}{\partial y}\right) \... 1answer 55 views Differential equation is not working I am trying to solve Differential equation, but its not working. Even, if I am using rhs=1, still it does not work. Any idea will help me a lot ... 1answer 73 views Nonatomic expression expected at position 1 in First[None] This is a follow-up question to an earlier question:Solving a system of PDEs on a piecewise polynomial domain. I tried to solve the system of equations from one of my previous post with the different ... 1answer 181 views Mathematica code for bifurcation diagram in 3D Good day. I need help with the code in mathematica to plot the bifurcation diagram (e vs z*) or (e vs x*), for the system ... 1answer 51 views Hybrid ODE simulation with very small parameters I am trying to solve a Hybrid dynamical system using NDSolve and WhenEvent. I am able to simulate when the parameters are close ... 0answers 37 views How to solve a system of five second order differential equations with boundary conditions? I want to solve system of five differential equations of second order with their respective boundary conditions. So, I create a function that depends on their solutions. Such as ... 1answer 47 views NDSolve Maxsteps Reached Error I'm trying to solve a system of Equations. The code is commented below, I am mainly conserved with the last few lines, specifically the NDSolve line. No matter what I do to the Maxsteps option, the ... 0answers 49 views Recommended model for hysteresis I have a fabric-based strain sensor and would like to find out what other recommended models can be used in the hysteresis modelling. I have tried using the cubic function for loading and unloading ... 3answers 191 views Include boundary conditions in wave equation solver I'm solving a wave equation using mathematica. I already included the initial displacement and velocity. However, I don't seem to be able to include boundary conditions u(-\pi,t)=u(\pi,t)=0. ... 1answer 56 views Mathematica crashes with non-integer exponents using NDSolve I want to solve a system of coupled PDEs. It works fine if I set i=0. (i is in the exponent of the PDEs) or i=1. in the code. However, if I set, e.g., i=0.1 NDSolve crashes after a few seconds.... 2answers 57 views Solving two parametric ODEs and then plotting a curve derived from the solutions with respect to the parameter I have the following code ... 0answers 50 views Solving ODEs in several variables for a single function? Consider differential equations such as ... 1answer 105 views Stabilized Inverted Pendulum Blog Post Broken in 12.0? One of the old Wolfram blog posts that I use frequently is this demonstration of the LQR gains computation. https://blog.wolfram.com/2011/01/19/stabilized-inverted-pendulum/ I've been able to trust ... 0answers 231 views Solving Maxwell's Equations in Mathematica For the sake of demonstration (for my students) and practice, I wanted to numerically calculate the electric and magnetic field (3D) for a sphere of uniform density moving slightly to the right and ... 1answer 82 views How to solve set of linear differential equation in Mathematica? I have a set of linear differential equations and are written in this format [X']=[Y]-[R] where [P][Y]=[Q] My actual P matrix size is of 20x20 and Q is of 20x1 and Y is of 20x1. I have written this ... 1answer 50 views How do I formulate a Dirichlet boundary condition for which the boundary depends on the other variable? I am trying to solve the Poisson equation on a cylindrical grid.$$ \frac{1}{r^2} \frac{\partial}{\partial r} r^2 \frac{\partial f(r, \theta)}{\partial r} = n(r, \theta)$$Analytically, there is ... 1answer 53 views Asymptotic solution of a second-order ODE containing InverseFunction Essentially, I have a second-order differential equation given by ode below. In order to solve it, I need to obtain an asymptotic solution where$g(x)$must vanish at infinity which will be used after ... 2answers 99 views Trouble second-order ordinary differential equations with integral terms I am a beginner of mma. During the learning of differential equations, I encountered a very difficult problem, a second-order system of ordinary differential equations with integral terms. This ... 1answer 235 views Neumann boundary condition is not satisfied I want to solve the diffusion equation on a disk centered at (0,0) with a radius of 1. I also want the flux at a radius of 0.8 to be zero. I have this initial condition at time zero: ... 1answer 377 views Can NDSolve address spherical gravitational collapse? As far as I know spherical gravitational collapse -of central importance to theoretical physics- is thought to be out of the scope of Wolfram Mathematica. However there are cases, as in this article,... 1answer 73 views Coupling DirichletCondition of one dependent variable to the value of the second Maybe due to my limited experience with PDEs solving I could not find the answer to the following issue. Let's say we have a simple advection along a line: ... 2answers 150 views How to use NDSolve with limited RAM? How can I use NDSolve when running out of RAM? The code I am implementing: ... 0answers 43 views Slope Fields in Mathematica and Sketching Appropriate Solution Curves How would I plot the differential equation dv/dt = 32-1.6v, where v(0)=0 I also need to solve for the limiting velocity. I am having a hard time figuring out how to find the limiting velocity. I ... 1answer 103 views Shooting Method for Numerical Solution I am trying to solve the following nonlinear differential equation using the shooting method. The equation is a boundary value problem with boundary condition x=Pi and x[Infinity]=0. In order to ... 3answers 447 views Compare FEM mesh with the mesh created within Mathematica This is a follow-up question to an earlier question: Make uniform mesh with quad elements Question: How to solve system of equations with NDsolve on the mesh created in Ansys in order to compare it ... 1answer 74 views Simplifying$\left(f\left(x\right)\frac{\partial}{\partial x}\right)^nf\left(x\right)\$ into a summation

In case you're wondering how to get differentials to act like operators in Mathematica, I stumbled across a package Carl Woll made to solve this issue in this question. There's a a more recent version ...
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Using MinValue with NDSolve

A simplified example looks like this. The basic idea is to maximize fHelper by adjusting \[Alpha] for each ...
67 views

Unable to use ElementMarker in DirichletCondition with structured quad mesh

I would like to use ElementMarker in a DirichletCondition on a structured quad mesh, but I am receiving the error: ...
807 views

Simulating a partial differential equation - reaction-diffusion systems and Turing patterns

I want simulate a reaction-diffusion system described by a PDE called the FitzHugh–Nagumo equation. The system that has been proposed by Alan Turing as a model of animal coat pattern formation and is ...