# Tag Info

Accepted

### Why do we solve non-linearity in hyperbolic PDEs that way?

The good thing about the conservative form is that this comprises multiple models, such as Shallow Water Equations, Euler Equations or traffic models. An essential feature of hyperbolic equations is ...
• 1,083
Accepted

### How to solve the problem without using symbolic computation

You can solve this numerically in Python without symbolic computation. from __future__ import print_function, division import numpy as np from numpy import exp from scipy.integrate import quad from ...

### Limitations with dynamical systems vs. PDEs?

PDEs are a form of dynamical system where there is another continuous variable. Usually this is space, so you're looking at how things over time and space instead of just over time. Here's an ...
• 12.3k

### Jacobians with automatic differentiation

Julia has a whole ecosystem for generating sparsity patterns and doing sparse automatic differentiation in a way that mixes with scientific computing and machine learning (or scientific machine ...
• 12.3k
Accepted

• 11.4k

### How does Mathematica compute real and complex solutions to single, non-polynomial equations?

As the other Answer already touches on the possibility of a symbolic root-solver being applied to this particular equation (by transforming into a polynomial form, albeit of degree $\ge 5$), I'll make ...
• 3,349