# Questions tagged [differential-equations]

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

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### 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 ...
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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: ...
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### 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 ...
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### Stiff system problems with NDSolve

I'm trying to solve the two order differential equations using NDSolve. Here is the code: ...
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### 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 ...
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### How can I Plot Phase Portraits Using ParametricNDSolve function(already know about StreamPlot function)?

I have a 2nd order ODE: $$\ddot{\phi}+3\dot{\phi}\sqrt{(\frac{8\pi G}{3})(\frac{1}{2}[\dot{\phi}^{2}+m^{2}\phi^{2}])}+\phi m^{2}=0.$$ I can use the StreamPlot command by breaking the ODE into a set of ...
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### I have a problem evaluating an ODE in Mathematica, where the error asks me to define a dependent variable?

I am trying to solve a series of linked ODEs in Mathematica (where the system describes the trajectory of a ball through the air). ...
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### Assigning A Symbol To A Second DSolve Solution

I am looking for a way to compress a lengthy DSolve solution to a single symbol, kind of like assigning a variable. I have this expression: ...
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### Supplying a seed for an iterative method in LinearSolve

Just a quick question. Does anyone know if it is possible to supply a seed for the iterative methods in LinearSolve? I have a large sparse system, and even using some Krylov iterative solver, my ...
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### Matrix differential equation with DSolve doesn't work

I'm trying to solve matrix differential equation with DSolve, but I got an error. ...
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### Can mathematica numerically solve this system of coupled integro differential equations?

Here's my system: R(x,y,t) is the concentration of a chemical that's diffusing across the box. The disk is a mobile sink for the chemical, which absorbs it in proportion to its concentration. The ...
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### FEM 1D 3D region coupling - speed up coupling using boundary integration

I am working on a simulation of the heat equation involving a 3D solid simulation coupled to a 1D fluid simulation (convective term of heat equation). I am using the method of false transient as ...
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### How to calculate precise higher derivatives of ParametricNDSolve solution

Higher Derivatives of NDSolve don't match the results from DSolve solution, can I somehow increase the accuracy of numerical method to match arbitrarily high derivatives? Equation I am using ...
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### NDSolve unable to solve system of PDEs

I'm trying to solve a set of PDEs and am running into problems. The system is defined by: As can be seen, there are two dynamical equations for $\rho$ and $\phi$, but the equation for $v$ has no time ...
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### Routh-Hurwitz criterion not giving correct answer when done manually?

Consider the system: \begin{align} \frac{dS}{dt} &= \nu N -\frac{\beta S I}{N} + \xi R - \nu S\\ \frac{dE}{dt} &= \frac{\beta S I}{N}- \sigma E -\nu E \\[2ex] ...
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### Why DSolve solution to this PDE does not match NDSolve solution?

I was answering different question How Can I Visualize a PDE Boundary Condition? and in the process, found that DSOlve solution to the laplace PDE does not agree ...
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### System of PDE with integration conditions interior of domain

I am trying to solve this system of pde numerically. I am unable to find any method in Mathematica that can handle this problem. The issue is having this integration condition in the domain. I tried ...
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### How to extract the numerical values in the tables

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I have fitted a difference equation to some data and would now like to find a differential equation that matches the difference equation. The difference equation and differential equation are  y(n)=...