Complexity theory and differential equations

What is the computational complexity of a differential equation?
The computational complexity of the solution y of the differential equation y′(x) = f(x, y(x)), with the initial value y(0) = 0, relative to the computational complexity of the function f is investigated.
The Lipschitz condition on the function f is shown to play an important role in this problem..
What is the main purpose of differential equation?
The derivatives of the function define the rate of change of a function at a point.
It is mainly used in fields such as physics, engineering, biology and so on.
The primary purpose of the differential equation is the study of solutions that satisfy the equations and the properties of the solutions..
What is the theory of differential equations?
In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives.
In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, and the differential equation defines a relationship between the two..
Where is differential equations used in real life?
Ordinary differential equations applications in real life are used to calculate the movement or flow of electricity, motion of an object to and fro like a pendulum, to explain thermodynamics concepts.
Also, in medical terms, they are used to check the growth of diseases in graphical representation..
A differential equation calculates how something changes and how fast that happens, so a computer can predict future outputs.
This helps with: Designing simulations.
Improving problem-solving programs.
Differential equation models are used in many fields of applied physical science to describe the dynamic aspects of systems.
The typical dynamic variable is time, and if it is the only dynamic variable, the analysis will be based on an ordinary differential equation (ODE) model.
In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives.
In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, and the differential equation defines a relationship between the two.
Neural differential equations have applications to both deep learning and traditional mathematical modelling.
They offer memory efficiency, the ability to handle irregular data, strong priors on model space, high capacity function approximation, and draw on a deep well of theory on both sides.
Originally Answered: What is the intuition behind Differential Equations? It means the rate of change of an object, say, population, is proportional to the size of that object itself.
It is the most basic model of differential equation.

Mar 28, 2017This book discusses the complex theory of differential equations or more precisely, the theory of differential equations on complex-analytic Table of contentsAbout this book

Mechanism by which a celestial body generates a magnetic field

In physics, the dynamo theory proposes a mechanism by which a celestial body such as Earth or a star generates a magnetic field.
The dynamo theory describes the process through which a rotating, convecting, and electrically conducting fluid can maintain a magnetic field over astronomical time scales.
A dynamo is thought to be the source of the Earth's magnetic field and the magnetic fields of Mercury and the Jovian planets.

Complexity theory and differential equations

What is the computational complexity of a differential equation?

What is the main purpose of differential equation?

What is the theory of differential equations?

Where is differential equations used in real life?