What scientific calculations can python do?

Features of python for scientific computing:

1. The scientific library is very complete. (Recommended learning: Python video tutorial)

Scientific libraries: numpy, scipy. Plotting: matplotlib. Parallel: mpi4py. Debugging: pdb.

2. High efficiency.

If you can learn numpy (array feature, f2py) well, then your code execution efficiency will not be much worse than fortran and C. But if you don't use array well, the efficiency of the program you write will be poor. So after getting started, please be sure to spend enough time to understand the array class of numpy.

3. Easy to debug.

pdb is the best debugging tool I have ever seen, bar none. It gives you a cross-section directly at the program breakpoint, which only a text-interpreted language can do. It is no exaggeration to say that it only takes 1/10 of the time for you to develop a program in Python.

4. Others.

It is rich and unified, not as complex as C libraries (such as various Linux distributions). If you learn numpy well in python, you can do scientific calculations. Python's third-party libraries are comprehensive but not complicated. Python's class-based language features make it easier to develop on a larger scale than Fortran and others.

In numerical analysis, Runge-Kutta methods are an important type of implicit or explicit iterative method for the solution of nonlinear ordinary differential equations. These techniques were invented around 1900 by mathematicians Carl Runge and Martin Wilhelm Kutta.

Runge-Kutta method is a high-precision single-step algorithm widely used in engineering, including the famous Euler method, used for numerical solutions Differential Equations. Since this algorithm has high accuracy and measures are taken to suppress errors, its implementation principle is also relatively complex.

Gaussian integral is widely used in calculations such as probability theory and the unification of continuous Fourier transforms. It also appears in the definition of the error function. Although the error function does not have an elementary function, the Gaussian integral can be solved analytically through calculus. The Gaussian integral, sometimes called the probability integral, is the integral of the Gaussian function. It is named after the German mathematician and physicist Carl Friedrich Gauss.

The Lorenz Attractor and the system of equations derived from it were published by Edward Norton Lorenz in 1963, originally published in the Journal of Atmospheric Science It was proposed in the paper "Deterministic Nonperiodic Flow" in the journal Atmospheric Sciences, which is simplified from the convection volume equation that appears in the atmospheric equation.

This Lorenz model is not only important for nonlinear mathematics, but also has important implications for climate and weather forecasting. Planetary and stellar atmospheres may exhibit many different quasi-periodic states that, while completely deterministic, are prone to sudden, seemingly random changes that are clearly represented by models.

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