In this tutorial, I demonstrate how to solve boundary value differential equations using the Finite Difference Method in Python. Learn step-by-step how to implement this numerical technique, ...

ABSTRACT: The solution of the Riemann Problem (RP) for the one-dimensional (1D) non-linear Shallow Water Equations (SWEs) is known to produce four potential wave patterns for the scenario where the ...

Abstract: This paper presents a finite difference method for the design of gradient coil in MRI. In this method, a linear matrix equation is formulated using a finite-difference approximation of the ...

ABSTRACT: This paper presents a comprehensive numerical study of the two-dimensional time-dependent heat conduction equation using the Forward Time Centered Space (FTCS) finite difference scheme. The ...

Electromagnetic (EM) Logging While Drilling (LWD) plays an increasingly significant role in oil and gas exploration and development. Fast and accurate simulation of EM LWD is essential for optimizing ...

Visual Studio Code (VSCode) is a powerful, free source-code editor that makes it easy to write and run Python code. This guide will walk you through setting up VSCode for Python development, step by ...

In numerous physical and biological systems, differential equations with parameters are commonly used to model specific behaviors or phenomena. These parameters frequently represent physical ...

A new approach in the finite difference framework is developed, which consists of three steps: choosing the dimension of the local approximation subspace, constructing a vector basis for this subspace ...