Questions tagged [differential-equations]

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

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36 views

Change of variables in 2-nd order PDE

I need to solve the following equation: $-(1+x) \partial_t ^2 \psi + (1-2x^2)\partial_x\partial_t \psi +(1-x)x^2\partial_x^2 \psi -2x \partial_t\psi+x(2-3x)\partial_x\psi=0$ for the function $\psi(t,x)...
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1answer
75 views

Non- linear ODE

I was working on this equation but I can't get out something for this: ...
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0answers
66 views

Checking whether the solution satisfies the equation

I want to check whether the solution f[u,v] satisfies the PDE. (As I know, all parameters are reals. So, I used Assumptions or ...
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0answers
54 views

Unable to implement boundary conditions for a spherical wave equation coupled to a Laplace equation

I am having trouble setting up in Mathematica v 12.1 the following system of coupled pdes on $r\in[0,10]$ $$ \left(\partial_t^2 - \frac{1}{r^2}\partial_r r^2 \partial_r \right) \theta(t,r) = -(1+2\Phi(...
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2answers
150 views

Is it possible to find a non-zero solution of an ODE?

Is it possible to solve the 4th-order ode analytically? ...
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28 views

NDSolve::derlen: The length of the derivative operator Derivative[1,0] in (T^(1,0))[\[Chi]2[t],\[Chi]1[z]] is not the same as the number of arguments [closed]

To be honest I have no idea how to handle three different DE inside NDSolve. Any help would mean a lot. ...
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3answers
143 views

Looking for intuition as to what numerical issue makes this solution of NDSolve blow up unphysically

I am solving the spherically symmetric wave equation in 3 dimensions on $r\in[0,2\pi]$ $$(\partial_t^2 - \frac{1}{r^2} \partial_r r^2 \partial_r) \theta(t,r)=0$$ with initial conditions $\theta(0,r)=e^...
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79 views

NDSolve gives different result if I use NeumannValue to set initial condition

While trying to get familiar with the NeumannValue function I tried solving the wave equation on $r\in [0,2\pi]$ for $\theta(t,r)$ $$\partial^2_t \theta - \partial^2_r \theta =0, $$ with intial ...
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1answer
103 views

Inconsistent behaviour between Active and Inactive forms of PDEs (finite element method)

I have been using the finite element tools in Mathematica version 13.0 to solve eigenvalue problems in physics (Schrödinger equation) using NDEigensystem, but I am having some issues with non-...
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0answers
41 views

Error in NonlinearModelFit for Complex differential Equation

I am trying to create a model that will fit data to a complex differential equation generated from NDSolve. The format that I have begins with ParametricNDSolveValue to find a general function where ...
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1answer
83 views

Manual Runge-Kutta 2 for a system of 4 ODE's

A follow-up on this question : I have the following system: $\frac{dx}{dt} = p_x \\ \frac{dy}{dt} = p_y \\ \frac{dp_x}{dt}=-\frac{\partial V}{\partial x} \\ \frac{dp_y}{dt}=-\frac{\partial V}{\partial ...
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2answers
273 views

Numerically solving the KdV equation

Backslide introduced in 9, persisting through 13. I am trying to solve the KdV equation numerically. The following code would work perfectly in version 5: ...
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0answers
58 views

Selecting specific solutions from a differential equation using DSolve with difficult boundary conditions

Let's suppose I want to solve Laplace's equation in Axial Symmetry: $$ \nabla^2\psi=\partial^2_{\rho}\psi+\partial^2_{z}\psi+\frac{1}{\rho}\partial_{\rho}\psi=0, $$ for some function $\psi=\psi(\rho,z)...
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1answer
88 views

Explicit integration of PDE running very slowly

I would like to solve the PDE $\frac{\partial u}{\partial t}=(1-x)\frac{\partial u}{\partial x}$, in the interval $[0,1]$, with initial condition $u(0,x)=e^{-218(\frac{-2}{3}-ln(1-x))^2}$, by manually ...
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1answer
56 views

ODE solution for a simple case

I was trying to solve this but I can't not fix the problem :( please help me. a,b,f and d positive vale. ...
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0answers
57 views

NDSolve complains about DAE being structurally singular

So I am trying to solve a simple system as defined bellow, but NDSolve keeps complaining. $(f'(t))^2 + (g'(t))^2 = 1$ $(\pi/2 - t)^2 = (\cos(2t) - f(t))^2 + (g(t) + \sin(2t))^2$ where $t\in[0,\pi/2]$ ...
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44 views

Equal equations or Expressions

I would like to check if equation (Sigmaa22) is the same as equation (stress) Basically i have 2 equations one is called Sigmaa 22 and the other one is called stress,My problem when i try to check if ...
5
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1answer
116 views

I understand mol but meet difficulty in understanding how `pdetoode` atumatically generate pde-to-ode-rules by using this strange pattern and rule?

I often solve pdes for my research, and years ago I found pdetoode in this forum is very handy. Although it is a small piece of code, it solves several interesting ...
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1answer
70 views

Writing a system of ODEs in vector form

I have the following system: $\frac{dx}{dt} = p_x \\ \frac{dy}{dt} = p_y \\ \frac{dp_x}{dt}=-\frac{\partial V}{\partial x} \\ \frac{dp_y}{dt}=-\frac{\partial V}{\partial y}$ ,where $V(x,y) = \frac{1}{...
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2answers
106 views

Mathematica: How can I solve the problem "The Kernel Local has quit (exited) during the course of an evaluation"

I am using a Mac Book with Monterey and 16GB RAM for a calculation with 2 nested For loops. I am relatively new to Mathematika and still trying to learn the language properly, so I hope the problem is ...
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0answers
109 views

A Simple equation [closed]

I don't know why is not working?!! ...
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1answer
67 views

DSolve wont solve

I have the following code to solve wave equations, but Dsolve doesnt give me anything, I would like to know why. ...
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5answers
130 views

DSolve with constant (e.g. $y'(x)=c x$)

I'm trying to solve the following problem: I already know the answer is $y(x) = x^2$, but how could I ask Mathematica to solve this for me? ...
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2answers
236 views

Using NDSolveValue for Solving a parabolic PDE numerically

Inspired by this question I am trying to solve the following PDE numerically on $x \in [-3, 3]$ and $t \in [0, 0.5]$ using NDSolveValue: $$ \frac{\partial p}{\partial t} = (12x^2-4) p + \left[4x(x^2-1)...
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1answer
71 views

NDSolve error: CoefficientArray:... is not a polynomial

I get strange errors (CoefficientArrays::poly and NDSolveValue::femper) with NDSolveValue: ...
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1answer
262 views

Are compound matrices implemented in mathematica?

Compound matrices are matrices whose entries are all the minors of a given size of another matrix. https://en.wikipedia.org/wiki/Compound_matrix https://www.researchgate.net/profile/James-Muldowney-2/...
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1answer
116 views

LaplaceTransform works well with x[t], but doesn't recognize x[1][t], how to make it works for x[1][t]?

Bug introduced in 12.2(?), persisting through 13.0. When I am solving odes using LaplaceTransform, I found that LaplaceTransform works well with u[t] or y[t] or x[...
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2answers
129 views

How to guide Eliminate or GroebnerBasis to reduce a set of simple odes to a single ode (which can be done by Laplace Transform)

Recently, I am trying to use Eliminate or GroebnerBasis to simplify a system of ODEs. I don't want the solution of ODEs. What I ...
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1answer
59 views

How to accelerate numerial inverse laplace transform for pdes of Euler-Bernoulli beam problem

Happy new year! :) Recently, I am practicing laplace transform technique for solving pdes. In this extemely helpful post, @xzczd mentioned that "The last step is to transform the solution back, ...
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1answer
77 views

some error without reason [closed]

I just start to work with this code but it is not running?! Clear["Global`*"] eqns = {y[x]^2 - ((1/52)*Sqrt[3]*y[x])Sqrt[y[x]^2 + (x)^-2/1000 - (69/100)] + ((49 (x)^-2)/100000) - (69/100) == ...
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0answers
87 views

Does current Mathematica capability allow solving PDEs (e.g. reaction diffusion equation) over surface of a mesh or surfaces

I came across this nice paper (https://arxiv.org/pdf/1605.01583.pdf) where the authors simulated a reaction diffusion system over the surface of a gecko, primarily to understand how various patterns ...
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3answers
116 views
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3answers
171 views

Eigenvalue problem with NDSolve

I am trying to solve the following system of linear ODEs. It is an eigenvalue problem. ...
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1answer
115 views

NDSolve Warning: an insufficient number of boundary conditions. However, all boundary conditions are defined

I am trying to solve the system of equations (momentum conservation, heat, and polymerization equations) in the Couette problem. There are two planes, the bottom is fixed, the top is moving with the ...
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1answer
161 views

Solving Lagrangian with Mathematica [closed]

I'm pretty new to Mathmatica but I'm trying to use it to find a Lagrangian and then find the equation of motion from the Lagrangian. Think the method is correct but I just cant seem to get the syntax ...
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0answers
78 views

Rational numbers in NDSolve

Is it possible to use NDSolve with Rational numbers instead of Real? I use all rational ...
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1answer
155 views

Find right end-point satisfying an integral constraint

I am solving the following system of first-order ODEs with a variable right-end point l1num and boundary condition at that point ...
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4answers
682 views

Does Mathematica evaluate Sqrt[1] to +1 or -1 in this differential equation?

This is known ode that DSolve generates a wrong extra solution. Been there since 2010. I do not know if this was posted about here before or not. If it was, will ...
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1answer
118 views

FEM derivative matrix construction

Assuming $A$ is a $3 \times 3$ matrix (and a function of $x$, and $z$) and $K_i, \beta_i$, and $\alpha(T)$ are known parameters, I need to solve the following equation, (with an implied sum over $\mu, ...
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0answers
62 views

Path of moon orbiting the Earth [closed]

I'm trying to make an animation showing the path of the moon orbiting around the earth, but I'm having some trouble plotting it. For some reason, Mathematica doesn't give me any error messages but ...
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2answers
61 views

How to make integrals of interpolated matrices constructed by other interpolated quantities?

I have the following code producing an interpolated unitary matrix: ...
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0answers
62 views

Kolmogorov forward equation with Mixed Dirichlet Neumann problem

I am trying to solve symbolically the Kolmogorov forward equation for the transition probability p(x,y,t), viz, ...
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1answer
167 views

1D-waveequation with absorbing boundary condition: FEM solution?

I try to simulate the special absorbing(?) boundary condition `Derivative[1, 0][y][1, t] + Derivative[0, 1 ][y][1, t] == 0` which only allows energy flow in ...
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0answers
57 views

Exclude a term in a differential equation

How can I exclude this term (The red box) from derivation to make it consider it as a constant (Just a constant to be multiplied ), I am getting the differentiation for the whole equation but I want a ...
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0answers
92 views

Avoiding instability and missing boundary condition errors when solving a system of 3 differential equations

I am trying to solve this system of equations: dw(v,t)/dt =2g(v,t) w(t,v) g(t,v)= Pi/2 (v^2)d g0(v,t)/dt d go(v,t)/dt + d/dv[dw/dt *1/v^3)]=0 with initial ...
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1answer
108 views

Functions can graph but can't solve for partial derivatives

First I got a function g[xo,yo] by solving a system of partial differential equations ...
2
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1answer
99 views

Solving boundary value problem with coupled odes at interface

I am trying to get the eigenvalues of the following differential system ...
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0answers
226 views

3D stable fluids algorithm to simulate transition from laminar to turbulent flow

This algorithm is 3D extension of our 2D algorithm published on this page and here. We suppose that with this code we can simulate transition from laminar to turbulent flow. In this example we compute ...
5
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2answers
514 views

Numerical solutions of active 1D wave equations

I would like to solve the following PDE with finite difference method. The PDE is from the following paper, (https://arxiv.org/pdf/1911.11823.pdf). I would like to implement the algorithm for the left ...
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2answers
88 views

Heun functions and boundary conditions

Using the Mathematica Heun functions, is there are simple way to get the solution of the same equation satisfied by HeunG[z], but with the boundary condition $f(z=0)...

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