Questions tagged [differential-equations]

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

Filter by
Sorted by
Tagged with
-1
votes
2answers
59 views

Have been getting this error "NDSolve::ndsz: At z == 0.8068293549897082`, step size is effectively zero; singularity or stiff system suspected."

Tried googling the error "step size is effectively zero; singularity or stiff system suspected". Haven't found any soln. Any help would mean a lot. Posting the full code. ...
0
votes
0answers
26 views

Comparing parameter regimes workflow

I have some code that relies on some parameters. I pick a set of parameters, calculate some things, solve some differential equations then plot various things with the solution. Ideally I'd like to ...
2
votes
0answers
37 views

Problems with plotting interpolating function derived from NDSolve`ProcessSolutions

I am trying a simple test of plotting an interpolating function derived from numerical solution to heat equation using NDSolveProcessEquations, NDSolveIterate and ...
0
votes
0answers
57 views

System of stochastic differential equations

Is it possible to solve numerically system of coupled non-linear differential equations with noise? The system looks like ...
12
votes
2answers
1k views

How can I use fast Fourier transform (FFT) to solve a PDE (heat equation)?

I'm trying to solve a one-dimensional heat equation (PDE) with the Fourier transform numerically, in the way it was done here. The equation: , is subject to the initial condition: , where U(x,t) is ...
-2
votes
1answer
77 views

Solving differential equation - Bessel structure [closed]

I am trying to solve the following differential equation in Mathematica. It is giving the same results regardless of the domain that I give as input. $$ \phi''[...
0
votes
0answers
39 views

How to put piecewise constant control, dependant on the solution, inside NDSolve?

I am working on a Chemostat model with piecewise constant control ...
3
votes
2answers
333 views

Euler-method implementation

How can I implement this pseudocode in Mathematica? Algorithm: ...
0
votes
0answers
57 views

NDsolve for a vector valued function and NDsolve::ndfdmc error

I'm trying to solve numerically an ODE system written in a matrix form where I encounter an error: The simplified example: ...
5
votes
1answer
129 views

What Does this Syntax Mean in Ouput from DSolve?

When I run the code DSolve[y*D[f[x, y, z], z] - z*D[f[x, y, z], y] == 0, f[x, y, z], {x, y, z}] I get the following output. I don't understand this syntax. I ...
4
votes
1answer
125 views

How to solve Coupled a Parabolic and Elliptic PDE in NDSolve?

I want to solve a mixed PDE Parabolic-Elliptic system in 3-dimension (rectangular coordinate), as shown below: The respective code version with parameters value, boundary and initial conditions is, <...
4
votes
1answer
92 views

Problem with non-linear system of PDEs

I wish to solve the following system of hyperbolic PDEs: $\frac{\partial y}{\partial u}=\alpha \sqrt{2y-y^2}$, $\frac{\partial y}{\partial v}=-\frac{1}{\alpha}\frac{\partial\alpha}{\partial v}\:\left(...
0
votes
0answers
44 views

Replacing variables with values in a DisplayFormula

Something I cannot figure out and can't find clear or similar answers to what I want to do: I have created a Styled Notebook and in an Inline Formula cell have assigned some variables, for example <...
0
votes
1answer
61 views

How to NDSolve system with motion integral?

I deal with set of ODE, which looks like f'[i][t] = c + Sum[G[f[j][t]-f[i][t]], {j, 1, N}] where G[t] is smooth differentiable ...
0
votes
0answers
120 views

BVPh2.0 package

Is it possible to use BVPh2.0 package to solve ODE system of initial value problems? I need to solve an ODE IVP system using homotopy analysis method. I came through this package for solving the BVPs. ...
1
vote
3answers
113 views

Analytical solution of second order linear differential equation with boundary at infinity

I am a new user to Mathematica and I would like to solve a simple second-order differential equation as follow: $y''[x]+\frac{(D-1)}{x}\times y'[x]=k\times y[x]$, where $D$ and $k$ are just two ...
2
votes
2answers
141 views

Showing that a Hopf bifurcation exists?

I have the following system of ODEs: dx/dt = a/(1 + z) - Q*z dy/dt = Qx - qy dz/dt = qy - cz/(K + z). Assuming K = 1, Q = q < c, and a = c*(Sqrt[c/Q] - 1), is there a way to use Mathematica to test ...
1
vote
1answer
171 views

Incorrect results of DSolve

Finding a fundamental solution of a certain linear partial differential operator, I try ...
0
votes
1answer
81 views

Plotting a phase plane portrait of an oscillatory system?

I am trying to plot a phase plane portrait of the following system: dQ/dt = v*(z - Q)*(w^2 + Q^2)/(1 + Q^2) - Q dz/dt = k - Q where v = 1, k = 0.2, and w = 0.05. So far, I have the following: ...
2
votes
1answer
60 views

NdSolveValue Freeze sensitive to initial condition

I am trying to solve the following system of non-linear differential equations: ...
0
votes
0answers
31 views

Loops for every time step on a time-dependent function coming from NDSolve

I have a time-dependent function a[t], which comes from solving various differential equations. Therefore, to obtain the different values of ...
3
votes
1answer
518 views

Why is Mathematica unable to solve this integral equation?

How to solve the following integral equation in Mathematica? eqn = y[x, z] == z + x*Integrate[y[t, v], {t, 0, 1}, {v, 0, 1}] sol = DSolveValue[eqn, y[x, z], {x, z}] ...
1
vote
0answers
75 views

How to solve ODEs using deep learning in Mathematica [closed]

I have a number of ODEs (58) with 16 parameters and 9 variables. I want to solve the ODEs to obtain the analytical relationship between the parameters and variables. It is obviously that the ODEs ...
0
votes
0answers
86 views

NDSolve a system of PDEs with Periodic Boundary Conditions

I would like to analyse the system of differential equations $\begin{equation} \begin{split} \partial_tf_0&=\frac{C_{\mathbf{r}}}{(1+\lambda)^2}\bigg[\bigg(1+\frac{\lambda^2}{2}\bigg)\partial_{...
0
votes
0answers
27 views

How to visualize second order differential equations? [duplicate]

As we now we can use StreamPlot to visualize first-order differential equations like:y'[x]==1+x-y ...
0
votes
0answers
71 views

How to solve a system of nonlinear differential equations like this numerically

There are a set of nonlinear Bloch equations. ParametricNDSolve can not give the correct answer, how to deal with these equations? The desired answer should be (...
6
votes
1answer
83 views

NDSolve misses nontrivial solution

The initial value problem I would like to solve possesses an analytical solution ...
5
votes
1answer
130 views

Coupled pde for multiphysics joule heating with temperature dependent properties - error inconsistent dimensions

I want to simulate 3D joule heating and followed the wolfram multiphysics tutorial. This multiphysics problem is comprised of the equation for the voltage field: and the heat equation: with the ...
1
vote
0answers
77 views

Driving along a Beziercurve with given velocity

In this model I try to describe the kinematics of a point moving along a beziercurve b[u] (bezier parameter 0<u<1) with prescribed velocity ...
3
votes
1answer
127 views

Solving a differential equation where all functions are unknowns

I'm trying to solve DSolve[f[x]*(x^2*g''[x] - 2*g[x] + 2) + x*(x*g'[x] - 2*g[x])*f'[x] == 0, g[x], x] for $g(x)$, however Mathematica cannot find a solution. ...
0
votes
0answers
31 views

Errors while trying to do a change of variable

I have the following differential equation: $ \tag{1} \Delta^{-s}\frac{d}{dr}(\Delta^{s+1} \frac{d R(r)}{dr}) + (\frac{K^2 - 2 i s (r - M)K}{\Delta} + 4is \omega r - \lambda)R(r) = 0$ where $\Delta \...
2
votes
1answer
87 views

How to solve this set of integrated PDEs

Could anyone help me solve set of pdes with embedded integration? The pdes below is solvable , but can not be solved when I tried different parameters such as ...
1
vote
1answer
52 views

NDSolve Encountered non-numerical value for a derivative at t == 0

I want to solve this no-linear differential equation system: $1.2 (1 + 20(r(t)^2 + 2^2 + 4 r(t) \sin(\phi(t)))^2) \ddot\phi(t) + \dot \phi(t) + \phi(t) = 50 \sin(4 t)$ $\textbf{If}$ ($|-r(t)\dot\...
0
votes
0answers
45 views

How can I set a find max value function with parameter in NDSolve

For example, Here is a NDSolve function with a parameter of w ...
-1
votes
1answer
39 views

ODE Cauchy problem [closed]

I want to prove that the followning Cauchy problem doesn't have solution: $y'(x)\sin(x)=y\ln(y),y(\frac{\pi}{2})=1$ I solved the ODE and i found: $\ln(|\ln(y)|)=\ln(|\tan(\frac{x}{2})|)+c$ When i put ...
0
votes
0answers
49 views

NDsolve taking value of previous time step

I am using de NDsolve code below: ...
0
votes
1answer
131 views

Equation of motion through the Lagrangian with Lagrange multipliers

I ask for advice, I'm a little confused. I have such a Lagrangian. $L=\frac{1}{2}m(\dot{x}^2+\dot{y}^2)-\lambda(2x^2+3y^2-1^2)$ Here $\lambda(2x^2+3y^2-1^2)$ is the constraint on the phase variables. ...
0
votes
2answers
82 views

Using NDsolve with WhenEvent is not working

I am trying to use WhenEvent in this nonlinear equation system: $\ddot r-\dot\phi^2r+9.8(\sin\phi-0.7\cos\phi)=0$ $1.2(1+20(r^2+2^2+4r\sin\phi)^2)\ddot\phi+\dot\phi+...
1
vote
1answer
55 views

NDsolve for No-Linear system getting "not a list of number" [closed]

I want to solve this No-Linear equation system: $1.2 (562500 + 1.2(r(t)^2 + 40^2 + 2r(t)40Sin(\phi(t)))) \phi(t)'' + 1030400\phi'(t) + 0.41\phi(t) =2Sin (4 t)$ $r''(t) - 0.7*9.8Cos(\phi(t)) + 9.8 ...
2
votes
1answer
180 views

DSolve fails to find solution based on elementary function

I have two differential equations for which DSolve does not find a solution, however, there are simple solutions in terms of elementary functions, and more ...
0
votes
1answer
74 views

Solve a differential system of equations in time

I am trying to solve a system of 3 equations and 3 unknown variables that change in time (Tw(t), Tcor(t), Texit(t)). ...
3
votes
1answer
82 views

How to verify series solution to an ode generated by AsymptoticDSolveValue?

To verify solution returned by DSolve, one can use the method shown in howto/CheckTheResultsOfDSolve.html and look for True (...
0
votes
2answers
78 views

Series solution to an ode does not satisfy initial conditions. Frobenius series. AsymptoticDSolveValue

I was trying to verify my solution to this ode using power series method. The expansion point is x=0. This ode has removable singularity, so Frobenius series and ...
3
votes
1answer
66 views

NDSolve unable to solve coupled ODE's after specific point

I am trying to solve a set of coupled differential equations that look like this ...
1
vote
1answer
104 views

Ordinary differential equation with variable (polynomial) coefficients -form of solution

If you have a differential equation with polynomial coefficients then quite remarkably Mathematica can find a solution. For example for the second order differential equation $ y''(t)+b y'(t)+\left(\...
1
vote
0answers
51 views

NDSolver cannot give precise result for extremely small values

I would like to solve an ODE with MMA. The equation is simply the Coulomb law. However, I cannot get a satisfying result: ...
5
votes
4answers
257 views

Any Mathematica techniques to calculate time takes to reach the equilibrium of a PDE solution

I am solving this PDE numerically (dimensions: spatial variable x and time t). I know how to solve my problem numerically (for a given range of time). The solution reaches its equilibrium after a ...
0
votes
1answer
82 views

Stiff system problems with NDSolve

I'm trying to solve the two order differential equations using NDSolve. Here is the code: ...
0
votes
2answers
179 views

How to plot poincare map as shown in below image for Duffing equation?

I am trying to plot phase diagram and poincare map. But I cannot get the poincare map as shown in the image below Phase Space ...