Questions tagged [differential-equations]

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

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System of nonlinear differential equations

I used the following commands: ...
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Differential equation system, Jacobian matrix, characteristic equation

We assume the differential equation system: $X'=σ(Y-X),Y'=X(ρ-Z)-Y,Z'=XY-βZ$. I can calculate the equilibrium points as: ...
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Plot global maximum point and differential equation

I have two questions: (1) I found the global maximum point of the following function ...
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Transient Heatflow in a Wheel Disc Brake

I try to model the Convection–diffusion equation for a rotating 3D annulus(small thickness): The temperature u[t,x,y,z] is described in cartesian coordinates. ...
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Simplifying solution to a third-order Boundary Value problem

I have been trying to solve a physical problem during which I reach the following third-order, Linear O.D.E. The solution I get using this expression is really messy. Is there any way to simplify it ...
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Could you help me convert my PDE into a boundary value problem?

This is my code. It works as an initial value problem, but I want to solve it as a boundary value problem. ...
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NDSolve::deqn: Equation or list of equations expected instead of eqns in the first argument eqns

I am new to Mathematica, actually, I am working on a project based on Swarm Intelligence. I am trying to run a simulation of sphere formation of 10 robots, but there is a problem in equations. Here is ...
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1DPoisson equation with Dirac delta

I was writing my own FEM method to solve the Poisson equation \begin{align} -u'' &= \exp(-c(x-1/2)^2)\\ u(0) &= u(1) = 0 \end{align} where c=100. and I'm reading from the book of Mats G. ...
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Using the results from NDSolve in another equation

I want to use the results sol returned from NDSolve (values of f at different ...
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Using GreenFunction in 2D free space for Laplacian

V 12. on windows. I have a question about using Mathematica's GreenFunction to verify known result for Green function for Laplacian in 2D. (I also have question ...
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More elegant/efficient numerical WKB implementation for 1D Schrödinger Equation

I'm trying to figure out a better way to implement numerical WKB quantization of a spectrum. WKB quantization is the condition that $$\oint_{E}p \, \mathrm{d}q = \pi \hbar (n+1/2)$$ So the idea to ...
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Allow Mathematica to solve the differential equations with larger than 16 digits parameters

Consider the system of differential equations ...