Questions tagged [differential-equations]

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

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Looking for an appropriate method of NDSolve for dynamical system

I am dealing with the numerical solutions of a variety of dynamical systems with integrals of motion. As the example, let me consider the Kuramoto model, which equations of motion are ...
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How to take a derivative of a function with respect to another function inside the function?

I have these two equations: ...
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1 answer
82 views

Numerical solution of an ordinary integro-differential equation

I am trying to solve the following integro-differential equation: $$ a(\varepsilon) f'(\varepsilon) + b(\varepsilon) f(\varepsilon) + \int_{\varepsilon}^{\varepsilon + \varepsilon_1} R_1(\epsilon) f(\...
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4 votes
4 answers
160 views

Parts of a Piecewise Matrix Function in NDSolve

First time posting. Reproducing the Problem I'm relatively new to Mathematica (using v.12.3), and working on a project. My problem can be reproduced with this. ...
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1 answer
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Plot for DSolve in mathematica [closed]

I don't Plot it's not working!!, can you help me? ...
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0 answers
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Neumann Boundary Condition for thermal radiation between two bodies

I'm trying to formulate and solve a pde which models thermal radiation between two bodies using a Neumann boundary condition. I've created a mesh and want to capture the thermal radiation heat ...
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1 vote
1 answer
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NDSolve divergence error

I am trying to solve an ODE using NDSolve, but get a divergence error. Could someone please help me wi it? The following is my code. ...
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1 answer
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Are derivatives from interpolating functions created by NDSolve using derivatives of the spline or numerics from solving DE

For example given the code: ...
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2 votes
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NDEigensystem returns reversed list of eigenfuctions

I'm considering the two coupled linear differential operators ...
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5 votes
1 answer
131 views

NeumannValue is producing incorrect results

Cross-posted in Wolfram community, an online Mathematica notebook is available there. The problem under investigation is solving the Laplacian equation to model seepage. See the image below for the ...
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3 votes
1 answer
102 views

Speeding up Boussinesq equations solving?

I am working on Boussinesq equation. The notebook can run perfectly for only 0.6 steps and then the calculation starts running slowly after 0.7. All boundary conditions seemed fine. I am unsure if I ...
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1 answer
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Numerical Plot for an example

I would like to compare the numerical and analytical solution with plot for this example but something is wrong I don't know how to fix it?!! ...
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2 votes
1 answer
47 views

Convert boundary condition involving derivative to NeumannValue programmatically

As discussed in e.g. what causes the error "The dependent variable in the boundary condition needs to be linear" when using NDSolve? When FiniteElement ...
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3 votes
1 answer
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Problem with NIntegrate a solution of NDSolve

I'm having trouble making a function that uses the result of NDSolve: ...
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How to use DEigensystem with Dirichlet Condition an NeumannValue

How can I use DEigensystem to obtain eigenvalues and eigenfunctions for differential operators in two dimensions for the follwing problem Examples in Wolfram documentation only consider Dirichlet <...
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2 votes
2 answers
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How to solve 2D eigenvalue problem with robin boundary conditions

I need to solve an eigenvalue problem in 2D as seen in the picture. I've tried the function NDEigensystem but reading its documentation it seems it has issues with ...
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Following differential equations are not solving in MATHEMATICA. using DSolve [closed]

I am trying to solve following differential equations with boundary conditions in MATHEMATICA by using code DSolve.
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3 votes
0 answers
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Understanding `NeumannValue`

From this interesting question Reveal the formal PDE of FiniteElement ...
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1 answer
115 views

Can Mathematica solve an ode asymptotically as x goes to infinity?

Given the following ode for $x\rightarrow\infty$: $$\left(x f(x)^3 \left(\frac{(x f^\prime)^\prime}{x}\right)^\prime\right)^\prime=0,$$ in the sense of "asymptotics", the equal sign is ...
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Numerical solution for multi-step PDEs

I am trying to numerically solve the following PDEs in MMA (v12.0) $$\partial_u f(x,u) = \left\{\begin{matrix}&-a f(x,u) + b \, \partial_x^2 f(x,u), & 0<u<T\\ &r(x;\alpha_1) \, f(...
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1 answer
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Find the parameter in NDSolve giving the desired solution

EDIT: I've edited many times because the system gives errors when the body is modified all at once. I've simplified the problem. The simplification consists of having reduced the number of parameters ...
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DSolve doesn't solve a second order differential equation

I am trying to solve an ordinary differential equation: ...
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5 votes
1 answer
223 views

Neumann boundary conditions are not satisfied

I am solving a system of 3 ODEs and I want to implement neumann BC (d/dx = 0 @x=0). However, the solution does not seem to obey neumann BC when parameter A1/A2/A3 is non zero, as I notice that the ...
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0 answers
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While using NDSolve, ven though I'm evaluating cell and getting no errors, I see no output [closed]

still very new to Mathematica. Even though Im not making any syntax errors, I get no outputs from this code: ...
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1 vote
2 answers
66 views

General solution of 2-nd order ODE with power-law term and parametric constants

I'm trying to get a general solution to the given differential equation. What substitution I'm supposed to apply to get the solution? ρ,Ω and ...
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Apply NDSolve(MethodOfLines) in predefined, fixed spatial mesh [closed]

I consider an approximativ solution of a pde problem in a given mesh and I would like to compare this solution with the one obtained bei NDSolve MethodOfLines in the same mesh ! Usualy ...
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7 votes
2 answers
277 views

Why does DSolve give 1/0 on this first-order Riccati ODE?

This is from a textbook. Why does DSolve give 1/0 using Mathematica v13.0.1 on Windows 10? Does it happen using other versions? ...
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BVP with 2nd order coupled ODEs

I get the following error messages: Infinite expression 1/0. encountered. Indeterminate expression 0.\ ComplexInfinity encountered. Encountered non-numerical value for a derivative at s == 0.1 ...
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3 votes
2 answers
134 views

How does NDSolve treat matrices?

I am having trouble trying to solve a differential equation which couples the elements of a matrix. Let's say I have the following ...
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1 answer
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How to solve this second-order nonlinear ordinary differential equation using the explicit runge kutta method [closed]

It its my first time using mathematica so I am very unfamiliar with the syntax. I have gathered pieces of codes to solve this system of second order non-linear Diff.Eq. : ...
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2 votes
2 answers
233 views

Solve differential equation with constant

How can I get a symbolic solution from the following differential equation? I don't know in that case using a change of variable is a good idea. I have tried in maple as well but the form of the ...
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1 answer
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invoke data in the NDSOLVE

...
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7 votes
1 answer
318 views

Reproducing figure from paper on hydrodynamics

I am trying to solve Eqn. on Page 674 of https://www.nature.com/articles/nphys3667.pdf I shall quote the relevant paragraph : Next, we proceed to analyse the nonlocal response in a strip with ...
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2 votes
1 answer
58 views

NDSolve: there are more variables than equations, underdet

I am working on using NDSolve to solve coupled ODE. The following is the coupled equations. It works fine for sever orders. I used table to generate like 962 couple variables and equations, where the ...
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3 votes
1 answer
153 views

Numerical solution of an advance-delay ODE with multiple advances and delays

I am trying to solve a differential equation of the form ...
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0 votes
1 answer
43 views

How to define a function of parameters of a DSolve output?

If I have some ODE that has some parameters, say $a$ and $k$, how would I define a function of those parameters of the solution DSolve. For example cosider the following code ...
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-3 votes
3 answers
120 views

Solution of initial value problem using fixed point iteration

I have to solve ODE x'(t)=1/2(x(t))-t, x(0) The existence of solutions of this IVP is equivalent to finding a fixed point of integral operator T:C[0,1]->C[0,1] defined by T(x(t))=x(0)+integral[0,t][...
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1 answer
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How can I solve a PDE on the real line with DSolve? [closed]

I would like to know if it is possible to solve a PDE on the real line by using DSolve. For exapmle cosider the heat equation $u_t=u_{xx}$, $u(x,0)=e^{-x^2}$ for $x \in \mathbb{R}$ the code I tried ...
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0 answers
59 views

I am unable to plot 3D graph of integral function

I am not able to solve this integral ...
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1 vote
2 answers
81 views

Can I take the Fourier transform of a PDE in both sides? [duplicate]

I want to know if it is possible to use a PDE in the function FourierTransform instead of a function. Consider for example the simple case for the heat equation ...
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0 answers
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NDSolve overdetermined but I can't see how

Edit: partial answer This confuses me but it is due to some behaviour of pattern matching which just seems wrong to me. An example of the behaviour ...
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1 vote
1 answer
77 views

Any one could help with this NDSolve?

I want to know the traces of electron and its velocity based on the equation ...
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4 votes
0 answers
75 views

NeumannValue nonlinear pde?

Inspired by the highly interesting question Solving Burger's equation with NDSolve at large time I'll try to understand Finite-Element-solution for nonlinear pde in more detail: Burger pde $u_t(x,t)+u(...
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4 votes
1 answer
139 views

NDEigensystem with FEM: parasitic solutions

I am trying to find the eigensystem of a system of 3 coupled ODEs. Analytically, the system spectrum should have a gap at [-2M,2M] (except for the degenerate state with E=0, strictly at the middle of ...
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9 votes
4 answers
732 views

Solving Burger's equation with NDSolve at large time

I want to solve the following Burger's equation $$\partial_tu+\partial_x\left(\frac{u^2}{2}\right)=0,~~x\in[0,2\pi],~t>0\\u(x,0)=\frac{1}{3}+\frac{2}{3}\sin(x)$$ with mathematica. Here's my code: <...
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1 vote
1 answer
103 views

Nonlinear Schrödinger Equation With Periodically Varying Function

I am trying to solve Equation. 42 from https://labsites.rochester.edu/agrawal/wp-content/uploads/2019/08/paper_2019_03.pdf The equation I am trying to solve is a nonlinear Schrödinger equation More ...
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0 votes
1 answer
49 views

Solution of NDSolve evaluates pointwise, but won't plot (possibly due to issue with FindRoot and replacement rules)

I'm trying to solve a pair of uncoupled differential equations using NDSolve, where the initial conditions are determined by FindRoot. Here's the relevant section of the code, including error message. ...
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2 votes
1 answer
53 views

Symbolic PDE manipulation

I'd like to transform a PDE in a way such that I can express a temporal derivative as a spatial derivative using some known relation. Very simple example: ...
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0 votes
0 answers
33 views

Giving a scalar and vector function to ND solve?

I'm trying to solve a coupled system of ODEs using NDSolve. In this system, one function is a scalar and another is a vector i.e. it contains multiple components. <...
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1 vote
0 answers
59 views

NDSolve and UnitStep function

I am reposting my question because I accidentally deleted the previous one instead of editing. I am trying to solve the system using NDSolve ...
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