# Questions tagged [differential-equations]

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

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### 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. ...
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### 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 ...
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### Problems with plotting interpolating function derived from NDSolveProcessSolutions

I am trying a simple test of plotting an interpolating function derived from numerical solution to heat equation using NDSolveProcessEquations, NDSolveIterate and ...
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### System of stochastic differential equations

Is it possible to solve numerically system of coupled non-linear differential equations with noise? The system looks like ...
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### 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 ...
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### 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''[...
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### How to put piecewise constant control, dependant on the solution, inside NDSolve?

I am working on a Chemostat model with piecewise constant control ...
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### Euler-method implementation

How can I implement this pseudocode in Mathematica? Algorithm: ...
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### 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: ...
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### 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 ...
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### 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, <...
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### 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 ...
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### 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 (...
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### NDSolve misses nontrivial solution

The initial value problem I would like to solve possesses an analytical solution ...
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### 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 ...
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### 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 ...
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### 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. ...
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### 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 ...
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### 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 ...
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### NDsolve taking value of previous time step

I am using de NDsolve code below: ...
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### 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. ...
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### 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 ...
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### 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)). ...
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### 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 (...
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### 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 ...
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### 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 ...
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### 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(\...
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### 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: ...
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 ...