Numerical simulations play a pivotal role in understanding complex systems governed by differential equations. Python, with its extensive libraries like SciPy, NumPy, and Matplotlib, provides a robust environment for simulating and analyzing ordinary and partial differential equations. This guide covers the essentials of setting up and conducting numerical simulations for ODEs and PDEs using Python.

Differential equations are at the heart of many engineering, physics, and mathematics problems. Python’s SciPy library offers powerful tools to solve these equations. This guide will walk you through solving differential equations using SciPy, covering both ordinary and partial differential equations.

In this blog post, I will show you how to use scipy.optimize.least_squares to solve nonlinear least squares problems in Python. Nonlinear least squares problems are optimization problems where the objective function is a sum of squared residuals, and the residuals depend on some nonlinear function of the parameters. For example, suppose we have some data points (x, y) and we want to fit a curve of the form y = a * exp(b * x) + c, where a, b and c are the parameters to be estimated. This is a nonlinear least squares problem because the residuals are y…

In this blog post, I will show you how to use scipy curve_fit to fit a function with multiple independent variables. Curve fitting is a technique to find the best parameters for a model function that describes the relationship between a dependent variable and one or more independent variables. Scipy curve_fit is a function in the scipy.optimize module that performs non-linear least squares curve fitting.