Questions tagged [differential-equations]
Questions on the symbolic (DSolve, DifferentialRoot) and numerical (NDSolve) solutions of differential equations in Mathematica.
5,172
questions
2
votes
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
votes
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
votes
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...
...
1
vote
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 ...
0
votes
0answers
39 views
0
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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
votes
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 $$S(x) = 1 + \frac{...
1
vote
1answer
65 views
Error in definition of PeriodicBoundaryCondition?
The documentation for PeriodicBoundaryCondition (https://reference.wolfram.com/language/ref/PeriodicBoundaryCondition.html) has: Where it says $u ( x_{target} ) = a + b\ u ( f ( x_{target} ) )$, I ...
-1
votes
0answers
36 views
Phase portrait plotting by mathematica [duplicate]
I am trying to do the phase space plot of the following expression
$\frac{dy}{dt} = -0.006y (1-0.001 y^{2})^ {2.003} $
Anyone can suggest me an appropriate code in mathematica?
2
votes
1answer
83 views
NDSolve Convergence Issue for Coupled Field Problems
I have tried to use NDSolve to solve a coupled field Eqs (see the attached Codes). The MMA solver seems to failed to converge to the requested accuracy or precision within 100 iterations
...
1
vote
1answer
60 views
Solving this Second Order D.E
I'm trying to solve this second order D.E.
eq[t_] = x''[t] - (D[Log[solx[t]], t] + D[Log[Abs[D[x[t], t]]^2], t]) (x'[t]^2 + Abs[x'[t]]^2)
where:
...
0
votes
1answer
68 views
Random number in system of equations, solving using NDSolve & WhenEvent
I need to analyse the effect of random forcing on the system of coupled equations. For example, I have shown the equations below.
$$\begin{pmatrix} x1''\\x2''\\x3''\\x4''\\x5'' \end{pmatrix}
+ M_{(5 \...
0
votes
0answers
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:
...
1
vote
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
votes
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 ...
0
votes
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
votes
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 ...
0
votes
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
votes
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
votes
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
vote
1answer
75 views
Symbolic solution to periodic boundary conditions
Is it possible to get an analytical solution to the following problem? If so, how?
$$a w^{(1,0)}(x,t)+b w^{(0,1)}(x,t)=p(x)+g w(x,t)$$
$$I.C.: w(x,0)=0 | B.C.: w(0,t)=w(1,t) | x \in \left[0, 1\right]$...
2
votes
3answers
66 views
NDSolve with error that “Power::infy: Infinite expression 1/0.^0.4 encountered.”
Here is my code
...
0
votes
3answers
117 views
Revolution around the x-axis of solution to a nonlinear differential equation
I have the following differential equation:
$$\pi\cdot\text{y}(x)^2=\sqrt{1+\text{y}'(x)^2}\tag1$$
With the initial condition $\text{y}(0)=1$.
Now, I want to plot the solution in order to obtain the ...
-5
votes
0answers
42 views
0
votes
1answer
66 views
Solving three non-linear ODEs analytically in one variable
Any idea what is the best way to substitute to analytically solve these equations in y(x) ?
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3
votes
2answers
69 views
Trouble verifying a solution to a differential equation
I am reading a physics book which has discussed one approach towards solving the differential equation
$$
\frac{d^2 x(t)}{dt^2} = Cx(t)
$$
as follows:
Using Mathematica to solve the equation. I tried ...
1
vote
0answers
83 views
Why is there no heat being transfered in my program?
I have been working on this code and am new to this coding language. I have been trying to model the transfer of heat through a hot plastic being cooled in a water bath. For some reason I have not ...
1
vote
1answer
61 views
Missing integration constants in solution to PDE
I am attempting to obtain the analytical solution (if possible) to the following:
$$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)$$
...
1
vote
0answers
38 views
problem facing while solving a coupled differential equation [closed]
I am trying to solve coupled differential equations, inside which I have a function which I am getting by doing NIntegrate. The code is shown below:
...
0
votes
0answers
93 views
2
votes
1answer
80 views
How to solve a Matrix of ODEs
Hey could you help me solving this matrix of linear ODEs. This exercise comes from the book "Transport Phenomena" by Byrd, Stewart and Lightfoot [23.D.4]. I managed to get this matrix of ...
1
vote
2answers
45 views
Given data, how to FindFit for function that returns the Last of the “ValuesOnGrid” for InterpolatingFunctions returned by multiple NDSolve-s
I have tried both, NDSolve and ParametricNDSolve, to tackle the following problem without success. I have looked at 2 other SE ...
4
votes
2answers
228 views
NDSolve with equation system with unknown functions defined on different domains
Based on @xzczd's excellent answer on solving an equation system with unknown functions defined on different domains, I've tried to apply the same technique to a similar system shown below:
Equations:
...
14
votes
4answers
652 views
FEM: Why are the numerical solutions of field equations with D and Inactive[Div] and Inactive[Grad] different?
Suppose you have the DE
$$
\frac{d}{dx} \left(
c(x) \left[\frac{d}{dx}u(x)\right]
\right) + n(x) = 0
$$
and you want to solve for $u(x)$ with some BCs with given $c(x)$ and $n(x)$. I thought that ...
0
votes
1answer
89 views
NDSolve for system of PDEs -Error: fewer dependent variables!
I am trying to solve the equations below to find the breakthrough curve in an adsorption process:
...
1
vote
0answers
47 views
Write and solve n dimensional ODEs
I'm trying to solve a $2n$ system of ODEs. The equations have the following form
$$\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))}$$
can anyone ...
1
vote
0answers
31 views
Plotting solution to PDE is cutting off $ z $-axis [closed]
I am trying to plot the solution of a system of coupled PDEs however the result keeps on chopping off the z axis and I am not sure how to display the entire Z axis. How can I show the entire solution ...
1
vote
0answers
145 views
Can this boundary value problem leading to a partio-integral DE be solved using finite Fourier or any integral transform?
I asked the three-dimensional version of this problem here which lead to a trivial solution. I have now tried it in 2-D
$$\frac{\partial \theta_h}{\partial x} + b_h (\theta_h - \theta_w) = 0, \tag 1\\\...
2
votes
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
votes
1answer
78 views
Periodic extrapolation out of the domain of the solution of a PDE in two directions
As a prototypic problem
...
asked Jul 25 at 7:07
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7,7512 gold badges14 silver badges35 bronze badges
0
votes
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
votes
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
votes
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
votes
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
votes
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:
$$c_1 e^{...
2
votes
2answers
159 views
How to solve a nonlinear second order ODE
I want to solve this equation
y''[x] + a + b y[x] + c y[x]^2 == 0, y[ā] == 0, y'[ā] == 0
where a, ...
5
votes
1answer
488 views
Three dimensional Laplacian insulated on lateral faces and convectively exposed on transverse faces (updated)
I have the three dimensional Laplacian $\nabla^2 T(x,y,z)=0$ representing temperature distribution in a cuboid shaped wall which is exposed to two fluids flowing perpendicular to each other on either ...
2
votes
2answers
180 views
Laplace's equation with mixed boundary condition using separation of variables
The equation and boundary condition are defined in the picture where $T_1$, $T_2$, $T_3$, $k$ and $h$ are constant value.
I am trying to use variable separation to solve the problem.
If $T(x,y)$ ...
0
votes
1answer
108 views
How to solve a differential equation involving LaplaceTransform?
currently I'm working on a problem in which I need to solve an equation of the following form:
$$\mathcal{L}\left[\frac{\partial f(x,t) }{\partial x} + \frac{\partial f(x,t)}{\partial t}\right] = \...
0
votes
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 ...
