# Questions tagged [differential-equations]

For questions about solving, analyzing, or creating differential equations to model some system. If possible, include specific tags about the type of differential equation (e.g. [tag:pde], [tag:ode], [tag:stochastic-ode]).

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### Geometric integrators besides midpoint/Crank-Nicolson?

I have a first-order ODE $$\dot{x} = a(t) \times x, \quad x(0) \in\mathbb{R}^3.$$ with $\|a(t)\| = 1 \;\forall t$. Consequently, $\|x(t)\|=\|x(0)\|$ for all $t>0$. I would like this to be ...
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### How to solve second order coupled non linear differential equations

For a project I am doing, I have to solve the following system of differential equations numerically using my own code: $$x^2K'' = KH^2 + K(K^2-1)$$ and, $$x^2H'' = 2K^2H + \alpha H(H^2-x^2)$$ ...
92 views

### Numerical integrator for $a'(t)=e^{-a(t)}f(t)$

Suppose I know a function $f(t)$ and all its derivatives in $t$ in closed form. Given $a(0)$ and some $t_0>0$, I'm looking for an explicit integrator that can estimate $a(t_0)$, where $a(\cdot)$ ...
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### Solving the heat diffusion equation with source term

I am trying to solve the 1-D heat equation numerically with a variable source term. The system is basically a tank containing styrene in which it polymerizes to liberate heat. I have assumed that the ...
I am trying to solve a set of linear PDEs of the form $$F\left(\vec{y},\frac{\partial \vec{y}}{\partial x},\frac{\partial^2 \vec{y}}{\partial x^2},\frac{\partial \vec{y}}{\partial t}\right)=0.$$ To ...
Consider the following stochastic differential equation \begin{equation} dy=\left(A-\left(A+B\right)y\right)dt+C\sqrt{y\left(1-y\right)}dW\tag{1} \end{equation} where $A$, $B$ and $C$ are parameters ...