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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1answer
21 views

Stiff System of ODEs: NDSolve Convergence Issues

I have tried to use NDSolve for solving 4th order coupled ODEs problems (see the attached codes). The MMA solver fails to solve this problem. ...
2
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1answer
37 views

NDSolve Inconsistent equation dimensions

I am getting an error while trying to solve for a differential equation. It is saying "NDSolveValue::femper: PDE parsing error... Inconsistant equation dimensions." I was wondering if anyone ...
0
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1answer
53 views

How solve nonlinear equations by 14 unknowns?

This is my code, i want to solve system by 14 equations and 14 unknowns(rr list).But the code doesn't run... ...
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0answers
28 views

How to make DSolve express constants in terms of the unknown function [closed]

If I do DSolve[y'[x] == y[x], y[x], x] Mathematica returns {{y[x] -> E^x C[1]}} Is there a way to have it return this ...
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0answers
39 views

How to find T[R]?

This is a second question about the system: ...
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0answers
25 views

How to set correctly the initial conditions with Infinity?

I have two functions given by the following differential equation system: ...
3
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2answers
192 views

Finding the Period of a Limit Cycle

I'm interested in the periods of limit cycles of the Wilson-Cowan equations which have the form $$x'(t) = -x + S(ax(t) - by(t) +e)$$ $$y'(t) = -y + S(cx(t) - dy(t) + f)$$ where $$S(x) = 1 + \frac{...
1
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1answer
65 views

Error in definition of PeriodicBoundaryCondition?

The documentation for PeriodicBoundaryCondition (https://reference.wolfram.com/language/ref/PeriodicBoundaryCondition.html) has: Where it says $u ( x_{target} ) = a + b\ u ( f ( x_{target} ) )$, I ...
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0answers
36 views

Phase portrait plotting by mathematica [duplicate]

I am trying to do the phase space plot of the following expression $\frac{dy}{dt} = -0.006y (1-0.001 y^{2})^ {2.003} $ Anyone can suggest me an appropriate code in mathematica?
2
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1answer
83 views

NDSolve Convergence Issue for Coupled Field Problems

I have tried to use NDSolve to solve a coupled field Eqs (see the attached Codes). The MMA solver seems to failed to converge to the requested accuracy or precision within 100 iterations ...
1
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1answer
60 views

Solving this Second Order D.E

I'm trying to solve this second order D.E. eq[t_] = x''[t] - (D[Log[solx[t]], t] + D[Log[Abs[D[x[t], t]]^2], t]) (x'[t]^2 + Abs[x'[t]]^2) where: ...
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1answer
68 views

Random number in system of equations, solving using NDSolve & WhenEvent

I need to analyse the effect of random forcing on the system of coupled equations. For example, I have shown the equations below. $$\begin{pmatrix} x1''\\x2''\\x3''\\x4''\\x5'' \end{pmatrix} + M_{(5 \...
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34 views

Using RandomVariate in a NDSolve

I want to solve a version of the Langevin's equation using RandomVariante with a normal distribution. Therefore, I used the next code: ...
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2answers
100 views

Solving integro-differential equation [closed]

I would like to solve the integro-differential equation of the form $$\left( -n \int_0^b b db + \frac{i \Lambda l_P^2}{9V_c}\frac{d}{db}+b^2+k\right)\psi(b)=0.$$ I followed the steps in Solve an ...
0
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1answer
41 views

NDSolve: input a value for a parameter from a list of values

I have a parameter in an equation which has a different value at each step from a list of values calculated in a former NDSolve differential equation. While what I am trying to achieve is more ...
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0answers
27 views

Asymptotic Relation as Boundary Condition

I want to solve a system of non-linear second order differential equations. For some of the unknown functions there are boundary conditions that i know how to write them in Mathematica. One of the ...
5
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1answer
131 views

Mass Transport FEM Using Quad Mesh

This question is a follow-up to my previous question and an attempt to implement @Tim Laska's excellent approach of setting up an anisotropic quad mesh. I'm solving a similar problem to @Tim Laska's ...
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0answers
53 views

NDSolve and NIntegrate with parameters

I have a problem with a numeric computation. I should solve a numeric ODE and the rhs is a numeric parametric function that I find with several NIntegrate. I'd like ...
0
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0answers
30 views

problem with solving a simple third order differential equation [duplicate]

I just wrote a simple line of code to solve a third-order differential equation: DSolve[{y'''[x] + 4*y[x]==0, y[0]==1, y'[0]==2, y''[0]==0}, y[x], x] Then ...
2
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1answer
39 views

Solving system of coupled PDEs with method of lines

I'm trying to solve: $\partial _{z} U(z,t) = i \sqrt{d} P(z,t)$ $\partial _{t} P(z,t) = -P(z, t) + i \sqrt{d} U(z,t) + i \Omega_{c}(t)S(z, t)$ $\partial _{t} S(z,t) = i \Omega_{c}(t)P(z, t)$ For the ...
1
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1answer
75 views

Symbolic solution to periodic boundary conditions

Is it possible to get an analytical solution to the following problem? If so, how? $$a w^{(1,0)}(x,t)+b w^{(0,1)}(x,t)=p(x)+g w(x,t)$$ $$I.C.: w(x,0)=0 | B.C.: w(0,t)=w(1,t) | x \in \left[0, 1\right]$...
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3answers
66 views

NDSolve with error that “Power::infy: Infinite expression 1/0.^0.4 encountered.”

Here is my code ...
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3answers
117 views

Revolution around the x-axis of solution to a nonlinear differential equation

I have the following differential equation: $$\pi\cdot\text{y}(x)^2=\sqrt{1+\text{y}'(x)^2}\tag1$$ With the initial condition $\text{y}(0)=1$. Now, I want to plot the solution in order to obtain the ...
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0answers
42 views

How do I solve the differential equation

I am unable to solve the differential equation. Plz, help.
0
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1answer
66 views

Solving three non-linear ODEs analytically in one variable

Any idea what is the best way to substitute to analytically solve these equations in y(x) ? ...
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2answers
69 views

Trouble verifying a solution to a differential equation

I am reading a physics book which has discussed one approach towards solving the differential equation $$ \frac{d^2 x(t)}{dt^2} = Cx(t) $$ as follows: Using Mathematica to solve the equation. I tried ...
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0answers
83 views

Why is there no heat being transfered in my program?

I have been working on this code and am new to this coding language. I have been trying to model the transfer of heat through a hot plastic being cooled in a water bath. For some reason I have not ...
1
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1answer
61 views

Missing integration constants in solution to PDE

I am attempting to obtain the analytical solution (if possible) to the following: $$a w^{(1,0)}(x,t)+b w^{(0,1)}(x,t)=p(x)+g w(x,t)$$ $$I.C.: w(x,0)=0 | B.C.: w(0,t)=z(t)$$ ...
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0answers
38 views

problem facing while solving a coupled differential equation [closed]

I am trying to solve coupled differential equations, inside which I have a function which I am getting by doing NIntegrate. The code is shown below: ...
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0answers
93 views

Why the following set of ODEs is not integrated?

Consider the following dataset: ...
2
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1answer
80 views

How to solve a Matrix of ODEs

Hey could you help me solving this matrix of linear ODEs. This exercise comes from the book "Transport Phenomena" by Byrd, Stewart and Lightfoot [23.D.4]. I managed to get this matrix of ...
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2answers
45 views

Given data, how to FindFit for function that returns the Last of the “ValuesOnGrid” for InterpolatingFunctions returned by multiple NDSolve-s

I have tried both, NDSolve and ParametricNDSolve, to tackle the following problem without success. I have looked at 2 other SE ...
4
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2answers
228 views

NDSolve with equation system with unknown functions defined on different domains

Based on @xzczd's excellent answer on solving an equation system with unknown functions defined on different domains, I've tried to apply the same technique to a similar system shown below: Equations: ...
14
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4answers
652 views

FEM: Why are the numerical solutions of field equations with D and Inactive[Div] and Inactive[Grad] different?

Suppose you have the DE $$ \frac{d}{dx} \left( c(x) \left[\frac{d}{dx}u(x)\right] \right) + n(x) = 0 $$ and you want to solve for $u(x)$ with some BCs with given $c(x)$ and $n(x)$. I thought that ...
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1answer
89 views

NDSolve for system of PDEs -Error: fewer dependent variables!

I am trying to solve the equations below to find the breakthrough curve in an adsorption process: ...
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0answers
47 views

Write and solve n dimensional ODEs

I'm trying to solve a $2n$ system of ODEs. The equations have the following form $$\frac{dx_i}{dt}=y_i-\sum_j(x_j-1)$$ $$\frac{dy_i}{dt}=-y_i+\frac{1}{1+exp(x_i(y_i-\sum_{j\neq i}y_j))}$$ can anyone ...
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0answers
31 views

Plotting solution to PDE is cutting off $ z $-axis [closed]

I am trying to plot the solution of a system of coupled PDEs however the result keeps on chopping off the z axis and I am not sure how to display the entire Z axis. How can I show the entire solution ...
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0answers
145 views

Can this boundary value problem leading to a partio-integral DE be solved using finite Fourier or any integral transform?

I asked the three-dimensional version of this problem here which lead to a trivial solution. I have now tried it in 2-D $$\frac{\partial \theta_h}{\partial x} + b_h (\theta_h - \theta_w) = 0, \tag 1\\\...
2
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1answer
81 views

ToElementMesh Error/General meshing strategies

I am trying to create a mesh using ToBoundaryMesh as opposed to DiscretizeRegion. I was hoping this would be a better strategy ...
4
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1answer
78 views
0
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1answer
56 views

How to plot a system of coupled PDEs using NDSolve [closed]

I am trying to solve the the following system of couples PDEs using NDSolve. However I am struggling to plot the solutions. I am trying to plot |u1[t,x]|^2 (i.e. the square of the absolute value) but ...
0
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0answers
49 views

Integrodifferential equation solving

I am trying to solve a integrodifferential equation in Mathematica, i.e., I'm trying to find a way to evaluate the code below, which isn't yet supported in mathematica, as far as I understand. ...
4
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1answer
145 views

How to solve the wave velocity in steel

In the simulation of stress wave propagation, I have the following two problems. First question: This question comes from page 69 of this book. The Lame equation for a linear elastic body without ...
7
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1answer
138 views

Sensitivity analysis of parameter on eigenvalues of predator-prey model

I am trying to do a sensitivity analysis of the parameter g on the eigenvalues of this simple predator-prey Lotka Volterra model. I know that this code is entirely ...
2
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1answer
61 views

Contradictory results for ODE in Mathematica [closed]

I am Solving the ODE $$x'(t)=A x(t)+w(t)$$ MMA gives a general result as $$x(t)\to e^{A t} \int_1^t e^{-A K[1]} w(K[1]) \, dK[1]+c_1 e^{A t}$$ Now I substitute $w(t)$ by $e^{-t}$, and obtain: $$c_1 e^{...
2
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2answers
159 views

How to solve a nonlinear second order ODE

I want to solve this equation y''[x] + a + b y[x] + c y[x]^2 == 0, y[∞] == 0, y'[∞] == 0 where a, ...
5
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1answer
488 views

Three dimensional Laplacian insulated on lateral faces and convectively exposed on transverse faces (updated)

I have the three dimensional Laplacian $\nabla^2 T(x,y,z)=0$ representing temperature distribution in a cuboid shaped wall which is exposed to two fluids flowing perpendicular to each other on either ...
2
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2answers
180 views

Laplace's equation with mixed boundary condition using separation of variables

The equation and boundary condition are defined in the picture where $T_1$, $T_2$, $T_3$, $k$ and $h$ are constant value. I am trying to use variable separation to solve the problem. If $T(x,y)$ ...
0
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1answer
108 views

How to solve a differential equation involving LaplaceTransform?

currently I'm working on a problem in which I need to solve an equation of the following form: $$\mathcal{L}\left[\frac{\partial f(x,t) }{\partial x} + \frac{\partial f(x,t)}{\partial t}\right] = \...
0
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0answers
33 views

Exiting CrossSlidingDiscontinuity in NDSolve to follow equilibrium curve

I am trying to figure out how to get the solution curve to an NDSolve to slide along once it reaches a boundary and then to exit the ...

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