Questions tagged [differential-equations]

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

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2
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0answers
134 views

Solving a Modified Biharmonic Equation on a Square

I am seeking to solve the differential equation \begin{equation} \left[\partial_{\overline{x}}^{4}+2\left(1+\delta\right)\partial_{\overline{x}}^{2}\partial_{\overline{y}}^{2}+\partial_{\overline{y}}^{...
0
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1answer
47 views

DSolve for System of Non-Homogeneous Differential Equation

Solve: x' = Ax + b Given: A = {{1, 2}, {3, 4}}; b = {{e^{t}},{2}}; This will solve if b == 0 DSolve[{x1'[t], x2'[t]} == a.{x1[t], x2[t]}, {x1[t], x2[t]}, t] But if ...
0
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1answer
27 views

ItoProcess with matrix of equations

What is the cleanest/simplest way to use ItoProcess to solve the equation $$i \text{d}\boldsymbol{\psi} = H\cdot\boldsymbol{\psi} \text{d}t + \boldsymbol{\psi}^2\...
7
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3answers
547 views

Solving heat equation on a cylinder with insulated ends and convective boundary conditions

I am trying to solve heat equation on a cylinder whose ends are thermally insulated and its circular face is exposed to convection. Therefore I have Neumann boundary condition on all faces of the ...
0
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0answers
32 views

Problems with NDSolve and initial conditions (NDSolve::nbnum1:)

this is the situation, I'm trying to solve a system (s1) with two differential equations, called "x[Ne]" and "y[Ne]". They have and initial condition that first need to satisfy ...
0
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1answer
54 views

How do I enforce this boundary condition?

I am solving this differential equation: (1 - 2 M/r) D[(1 - (2 M)/r) D[q[r], r], r] - (1 - 2 M/r) ((l (l + 1))/r^2 - (6 M)/r^3) q[r] with the boundary conditions ...
6
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3answers
328 views

Time dependent Schrödinger equation in 2D

I have the following Schrödinger equation in $2D$: \begin{cases} \partial_t \Psi(x,t) = V(x,t) \Psi(x,t) \quad x \in [-10,10]^2\\ \Psi(x,0)=\exp( \frac{1}{2} (-x^2+y^2)) \end{cases} where the ...
0
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1answer
61 views

Error in solving a system of partial differential equations

I'm trying to a solve of system of partial differential equation, but Mathematica is giving some error. Can anyone help me please to find out the error. ...
4
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2answers
99 views

Convert Derivative[1][f] to f'

I believe this is a little problem that everybody asking or answering ODE related question in this site suffers. We know derivative of a variable, say, f, can be ...
1
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1answer
48 views

Solving a Set of Differential Equations and just get the Equations Returned

Long time reader but first time asker for the Mathematica section. I'm trying to solve a set of differential equations and it just returns the equations back to me. I'm not entirely sure why, but ...
0
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1answer
54 views

How to fit the solution of a NSolve with a NDSolve embedded

I have a system : $$s'(t)=A n+B a(t)\\a'(t)=C s(t) $$ Then I define the function $\tau(n)$ as the solution of the equation : $$a(\tau(n))n=1$$ and I'm looking for the parameters $A,B,C$ with a fit. ...
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0answers
145 views

Fluid dynamics collapse 1D Euler equations with NDSolve

I am getting a solution with NDSolve for studying the collapse of an interstellar isothermal cloud. But I have two problems and questions: I am getting some warnings even if I am obtaining a good ...
3
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2answers
94 views

How to solve the following delayed differential equations with periodic delay effect?

I want to solve the following differential equations $\partial_{t} f(t) = - a f(t)-a \sum_{n=1}^{N} f(t-n \tau) \cdot \Theta(t-n \tau)$ I learned the way for solving the equations from the following ...
0
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0answers
47 views

Giving variable inside WhenEvent a value

I am defining ParametricNDSolveValue in one cell and then using this in another one to find the parameter value using bisection. For clarity, I have simplified my differential equation. In order to ...
0
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0answers
53 views

Solving Third order Differential equation

I just had This Third order differential equation but i don't got any idea how to solve it cause mathematica doesn't get me a straight answer does anyone got any idea? I just know from the paper i'm ...
0
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0answers
31 views

Error when using Manipulate[Plot]

I'm trying to create a plot that varies from m = 0.1 to m = 1 but when I use Manipulate, I can't get anything to show up and I get approximately 50 quintillion errors. I think it has something to do ...
1
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1answer
67 views

Ridges on Breather surface

BreatherSurface is given in Mathematica code. Taking clue from this view or otherwise how to obtain table of $ (u,v,x,y,z) $ points and its plot of any one single ridge where the cusps have infinite ...
0
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0answers
44 views

the number of equation does not match the number of variables

Excuse me , can you help me , please ? When i make run for this programme it give me a wrong that the number of equations does not match the number of variables ,,,, I try a lot on finding the wrong ...
2
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2answers
89 views

Super Slow Manipulate with Heat Equation - - Assumption, and Interpolate

Aim: solve coupled heat equation with cubic source, use DensityPlot and observe how system will react to changes in parameter(like kand ...
0
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1answer
53 views

Getting error when I substitute PDE for ODE

The following code works perfectly: ...
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0answers
31 views

I keep getting an error with NDSolve [closed]

I keep getting an error that says equations expected instead of True in the first argument but I put equations so I don't know if i just formatted or typed it wrong or what
0
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2answers
95 views

Better method for computing streamlines

Can someone suggest a better way to solve for streamlines? P.S. StreamPlot is not providing accurate results. Here, velocity is...
0
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0answers
38 views

Solving differential vector equations

I have this problem: A basketball is thrown from the top of a 50 m building horizontally at 30 ms−1. Find the kinetic energy of the basketball at t=1.8s This is the code i wrote ...
1
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0answers
88 views

PDE with boundary condition (differential equation)

I am trying to find a solution to this boundary value problem $$h_t= \frac{1}{2} \sigma^2 x^2 h_{xx} + r x h_x \quad s.t.\\ Ah(b,t)+Bh_x(b,t)=g(t),$$ where $A,B,\sigma,r,b$ are constants and $g(t)$ ...
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0answers
32 views

Solving coupled ODE (and simple ODE) for Friedmann equation with scalar field

I am trying to solve for a (simple) potential for the Friedmann equation and EOM for scalar field. Mathematically this means I attempting to solve coupled ODEs using NDSolve. But I'm having trouble ...
0
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1answer
84 views

coupled differential equations

I have to solve a set of coupled differential equations. First I have created a table containing all the equations and then solved using NDsolve. ...
5
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2answers
178 views

NonLinear system for chemotaxis

I want to solve the chemotaxis mode, given by the next non-linear system: It is taken from Murray's book: equation (11.30) at pag. 408 $$\frac{\partial n}{\partial t} = D \frac{\partial^2 n}{\partial ...
1
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1answer
55 views

Solve a ODE with specific conditions

I am trying to find (some) functions h(x,t) such that A h(b,t)+B h_x(b,t)=g(t), where A,B,b are constants and g(t) is a given function of time (h_x is the partial derivative w.r.t. the first component ...
0
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1answer
60 views

How can I plot 3-D system

If I have three equations nonlinear. I need to see the behavior around (0,0). How do I plot the three-dimensional system? Thank you in advance. I try to use this code ...
0
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1answer
52 views

Turn vector equation into matrix multiplication

I have physical equations of motion that describe the dependence of one vector field on the components of another vector field. Without getting too much into detail, my differential equations involve ...
4
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3answers
195 views

Geometrically nonlinear beam deflection

Edit only for those interested in large deflections of beams I discovered a mistake in the equations of the original question (below): in the normal force (compression/traction) ...
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0answers
33 views
2
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1answer
52 views

NDSolve matrix of differential equations

If I have a system of differential equations that I can write in matrix form $$\frac{\text{d}\mathbf{X}(t)}{\text{d}t} = \mathbf{A}\cdot \mathbf{X}(t),$$ with known initial conditions ($\mathbf{X}(0)=\...
1
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1answer
76 views

how to define an example of ODE that represents an undamped forced oscillator whose time evolution is described by beats

I am a newbie in Mathematica and I really don't know how to define an example of ODE that represents an undamped forced oscillator
0
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1answer
50 views

Changing the dependent variable

I'm using NDSolve to solve a set of ordinary differential equations. The output is something like. ...
0
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0answers
58 views

solving coupled non linear differential equations

I have to solve a set of non linear differential equations. I have generated the equations by this: ...
2
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1answer
118 views

Bug in DSolve when solving a system of two second order PDEs?

I'm solving a simple system of PDEs in Mathematica 11.1: DSolve[{D[f[x, y], x, y] == 0, D[g[x, y], x, y] == 0}, {f[x, y], g[x, y]}, {x, y}] This gives: ...
5
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1answer
84 views

NDSolve: how the initial step of finding explicit derivatives can be avoided?

There are several posts here devoted to resolving the following error message of NDSolve (NDSolve::ntdvdae, ...
3
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1answer
68 views

Inactive[Grad] is lost when NDSolve parses PDE

I encountered this when trying to solve the PDE mentioned here. I've transformed the equation to the following: ...
0
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2answers
77 views

Error when using NDSolveValue. Lists are not the same shape

Please, help me with the following issue. I am solving the following system of the coupled PDEs with the following boundary conditions and initial conditions. After performing the following ...
1
vote
1answer
89 views

How to solve a 3D permanent conjugate heat transfer problem?

I want to solve this conjugate heat transfer problem on NDSolve but Mathematica always quits the Kernel. Can you help me? I do not know exactly how to use the numerical methods that are NDSolve method ...
1
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0answers
56 views

How can I make NDSolve aware of vectorial nature of an ODE?

I am trying to solve the equilibrium equation $\text{DIV } \mathbf P(\textbf{u}(x,y)) = \mathbf{f}$, where $\mathbf P$ is the stress tensor defined by $$ \mathbf P = \mathbf F + (1-\det\mathbf F)^...
4
votes
1answer
121 views

Steady state solution (1D) of nonlinear dispersal equation

Now I'm interested in the equation $$\frac{\partial }{\partial x}\Bigl(\text{sgn}(x) u \Big) +\frac{\partial}{\partial x} \Bigl[ u^2 \frac{\partial u}{\partial x} \Bigr] =0$$ with boundary conditions $...
1
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0answers
54 views

NDsolve Boundary Condition is a Function of the Solution

I am trying to solve something like Fick's Law using NDSolve: $$\frac{\partial \varphi}{\partial t}=\frac{\partial^2 \varphi}{\partial r^2}+F(r,t)$$ Subject to a ...
0
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2answers
81 views

Integral of a numerical second derivative

I need to find the integral $M(r)$ of a second derivative of equation $f(r)$ where this equation has only a numerical solution sol = NDSolve[f[r],...]. ...
0
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0answers
33 views

Newmark method to plot the displacement V/s time and phase plot of a plate

I am unable to plot the velocity V/s displacement plot (phase plot) of plate subjected to a dynamic load. I have generated the displacement V/s time plot, but the curve is not smooth. Also, my code ...
3
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1answer
67 views

How to increase the speed of NDsolve when using WhenEvent

I am trying to solve a set of ODE's with switching. I implemented using WhenEvents. ...
11
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2answers
399 views

Nonlinear dispersal equation modeling insect aggregation

I'm a newbie with Mathematica, I know it's a basic answer, but I can't solve the problem on my own. I have the following equation reflecting insect aggregation at low population densities (taken from ...
6
votes
2answers
232 views

Why do isolated large values of WorkingPrecision fail in NDSolve?

Executive Summary: Getting an accurate answer often depends on setting the WorkingPrecision high enough. Once it is high enough, though, I would expect that its ...
4
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1answer
74 views

WhenEvent in Stochastic Differential Equation

Is there a way to add events with WhenEvent or similar when using ItoProcess? Minimal example of my problem would be to change ...