Questions tagged [differential-equations]

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

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Dynamical PDE system tutorials

Which are some up-to-date tutorials or books on integrating dynamical PDE systems (involving chaos, Shock waves, etc.) with Mathematica 10.0?
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How to solve this partial differential equation for $f$?

I want Mathematica to solve for the function $f$. $f$ satisfies the following constraints. $\frac{\partial}{\partial x} f(x,y) = y$ $\frac{\partial}{\partial y} f(x,y) = x$ $f(0,0)=0$ It would ...
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106 views

Non-linear ODE from closed-loop system and Response

I started using Mathematica 12 and ran into difficulties. Namely, I want to compare the results of the calculation of a closed system from Simulink and in Mathematica. I rummaged around a bit on the ...
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Solving an algebraic-differential equation

I cannot find the relevant part in the documentation. Maybe you have a quick solution to my problem. Background Sometimes you want to propagate in time some system of ODEs, but not all the variables ...
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71 views

Update initial conditions recursively/sequentially within ParallelTable using NDSolve

I am modelling 3D motion of particles inside a force-field using second-order coupled PDEs, which I solve from time t=t0 to t=t1 with initial conditions x0,y0,z0. I have a total number of "particles" ...
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179 views

How to solve this differential equation analytically?

How can I DSolve the following differential equation? Is there an analytical answer to this equation? ...
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52 views

Evaluation functions with lower and upper limit ODE?

How do I find the numerical value of y at 0 and also at 1. Here is my code. I appreciate any help. ...
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1answer
70 views

Matrix of functions

I want to create a matrix of functions. As explained in this question, I can create a matrix of variables: ...
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66 views

1D transport equation with Neumann conditions

I'm trying to solve 2nd order differetntial equation of heat transfer-type in a finite system x<0,L>, in particular: ...
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2answers
56 views

Get the derivative function plot from a NDSolve solution

I been trying to plot the derivative function of j[t], being j'[t]. Here a look to the code. I would appreciate your help. Thank you ...
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Sensitivity analysis of a hybrid system (using WhenEvent) using ParametricNDSolve [closed]

I am trying to do a sensitivity analysis using ParametricNDSolve for a hybrid system. with the following event: ...
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220 views

DEigenvalues and NDEigenvalues return different values

In the following example, DEigenvalues and NDEigenvalues return different results despite having identical arguments. Does anyone know why? (I use Mathematica 11.3) ...
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why DSolve in V 12 returned an internal module variables with $ on them in this example?

Fyi, Reported to WRI in case it is a bug. [CASE:4288939] Is this supposed to happen? ...
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BVP of coupled ODEs with unknown initial values

I want to solve the following 2nd order coupled ODEs: $$ \begin{align} f^{\prime \prime} (r) + \frac{2}{r} f^{\prime} (r) + f (r) g (r)^2 - f (r) + f (r)^3 - \frac{1}{5} f (r)^5 &= 0 \\ g^...
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2answers
213 views

DSolve can not solve my PDE

I'm having some trouble using Dsolve to solve a partial differential equation. This is my code: ...
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1answer
124 views

Solving Coupled system of differential equation with NDSolve

I am solving a system with coupled system of differential equation to obtain the time evolution of two vectors. The problem stated here is equivalent to solving Landau Lifschitz Gilbert equationLLG ...
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71 views

Extracting a vector from NDSolve solution

I made an NDSolveValue to get the variable ff[t] ...
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1answer
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Nesting NDSolve, Manipulate and Plot functions

I have a system of differential equations that I'd like to solve for different values of a parameter. I am doing so, by ...
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2answers
81 views

From f[g[x,t]] to f[g]

How can you change f[g[x,t],t] to f[g,t] ? I have differential equations ...
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How to solve this DE to get a matrix?

I have this DE $ g^{m \bar{n}} g^{r\bar{p}} \partial_t {g}_{m r} \partial_t {g}_{\bar{n}\bar{p}} = X_{i\bar{j}}~ \partial_t{f}^i (t) ~ \partial_t{f}^\bar{j} (t) ~~~ ~~~~~~~~~~~~(*) $ Where ...
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1answer
99 views

ParametricNDSolve fails when I *don't* print the results

Some updates added to end. Truly minimal exampled added at top. Minimal example: ...
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Analogue for Maple's dchange - change of variables in differential expressions

Maple owns an interesting function called dchange which can change the variables of differential equations, but there seems to be no such function in Mathematica. ...
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1answer
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How to get the implicit solution of this PDE (Maple can but I don't manage with mathematica)?

I asked this question about the analytical solution of the PDE: $$\partial_t c=\partial_x((c-a)(c-b)\partial_xc) $$ And I was given the answer that Maple gives the following implicit form as a ...
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1answer
95 views

Suppressing analytical evaluation in NDSolve

I am trying to find a numerical solution to a set of coupled ODEs with NDSolve. Let us say $\boldsymbol{X}$ is a vector, and $\boldsymbol{F}$ is a non-linear vector ...
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2answers
590 views

Phase portrait of a system of differential equations

I have a set of characteristic equations, obtained by method of characteristics from Hamilton-Jacobi equation $$H(q,x) = (q^2-q)x+(1-q^2)x^2$$ $$\partial_s x = (2q-1)x-2qx^2$$ $$\partial_{-s} q = (q^...
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1answer
211 views

One term in non-linear equations prevents NDSolve to work

I am currently working on the stratification of the core of the planet Mercury, meaning the formation of a conductive layer at the top of the convective core, with a moving interface between both ...
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1answer
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How to vectorize this nonlinear ODE system for NDSolve?

I learned a long time ago that NDSolve can often be sped up by vectorizing systems of equations. I've got a problem now that seems ideal for this approach, but I ...
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1answer
56 views

Cross coupling in DirichletCondition not supported — conflict with documentation?

Mathematica 12.0.0.0 happily solves the trivial coupled differential system as follows: ...
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InverseFourierTransform takes me forever

I am trying to solve complicated PDEs using FourierTransfrom and InverseFourierTransform on Mathematica 12.0, but the code below does not give me a result. I do not get any error messages but the ...
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290 views

Solving Cahn-Hilliard equation: LinearSolve: Linear equation encountered that has no solution

I have built the Cahn-Hilliard Eqs. in MMA (Mixed Formulation, second order), However, it doesnot work in MMA using Finite Element. LinearSolve: Linear equation encountered that has no solution. And ...
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1answer
75 views

Can we construct our own NDSolve`StateData?

NDSolve can be broken into three stages: NDSolve`ProcessEquations processes the equations and sets up an NDSolve`StateData ...
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Constant positive and negative Gaussian curvature $K$ meridians as orthogonal trajectories

The plot code below depicts two point through which profiles of constant $K$ are drawn positive and negative. ...
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1answer
96 views

Reconstructing a function from its gradients

I have a list of the components of the gradients, $\partial f/\partial x_i$, of a function $f(x_1,x_2,\cdots)$. Is there some neat way to reconstruct the function $f$? One approach to doing this ...
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1answer
70 views

WhenEvent error in NDSolve ODEs

I wish to change the term, T'[t] to 0 when S[t]<=0 when I solve ODEs. I have used WhenEvent in my NDSolve part, but it seems not work. The code is ...
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325 views

Solving PDE with unreasonable results

I have a simplified version of my chemical reaction problem. Basically it solves the concentration (ca) and grain (g2) diameter. The ca function is depended on particle diameter R, while g2 function ...
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1answer
68 views

Solve 1D Wave Equation

I wanna model 1D wave equation and plot it, Here is my try so far, ...
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Manipulating a ParametricFunction to handle units

I have a pretty nice way to handle units on a result from NDSolve, which basically consists of converting all of the units to SI, stripping them, calling NDSolve, and then putting the units back. I'll ...
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1answer
95 views

Line-Dirichlet Boundary NDSolve

I have defined such a Dirichlet boundary conditions which fixes the nodes in a line, however, the results show that only two nodes are fixed, not the nodes in a line, Code: ...
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DSolve Varying Base on Implementation

I am trying to understand the behavior of a system of equations that is derived from: ...
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3answers
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Problem with module for solving wave equation

Im really new to mathematica and trying to solve a homogeneous wave equation numericallly. I wrote a module for it and wanted to test it but it only returns my input. ...
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1answer
59 views

Solve and plot PDE on restricted domain

I want Mathematica to solve (I used a picture since when I use mathjax code the editor here says I might be using wrongly formatted code...) So far, I have ...
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0answers
42 views

Error in PDE: Length of Derivative operator

I am trying to solve Poisson's equation in a cylinder with Dirichlet boundary conditions for the top, bottom, and sides of the cylinder, but I am getting the following error from NDSolve: ...
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1answer
104 views

Solving a nonlinear PDE

I'd like to know the asymptotic ($ t\to\infty $) behavior of $$ \partial_tu = -y\partial_{y}u + x^2 + y x \partial_xu - (1 + \partial_xu)^2 $$ with $ u(0, x, y) = 0 $. ...
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1answer
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NDSolve error with manipulate for 2 coupled ODEs

While trying to solve a system of coupled ODEs (for EVE[t] and FTZ[t]) with Manipulate, I ...
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PeriodicBoundaryConditions an a square

I hope the answer is simple, but I can't see the solution: I want to solve a PDE for u[x,y] under Periodic boundary conditions on say a square size 10 x 10. I.e. <...
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1answer
137 views

Wave equation: Understanding PeriodicBoundaryCondition

Inspired by the interesting question 202542 I try to solve the wave equation with coupled boundary conditions u[x,t==1 ]==u[x,t==x/2] I tried ...
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1answer
177 views

Fourier Collocation For Heat Equation [closed]

In fact My problem is this $$\frac{\partial u}{\partial t}+\ sin(y)\frac{\partial u}{\partial x}=\nu(\frac{\partial^2 u}{\partial x^2} +\frac{\partial^2 u}{\partial y^2})$$ But I wanted to test the ...
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1answer
56 views

Contour Plot of system of differential equation

I am trying to find the fixed points and plot the nullcline/contourplot for the system below, but I get conditional cases $$\frac{d\theta_1}{dt}= K sin(\theta_1 - \theta_2) - sin(\theta_1)$$ $$\frac{...