ABSTRACT: This study presents a comprehensive numerical investigation of fourth-order nonlinear boundary value problems (BVPs) using an efficient and accurate computational approach. The present work ...

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 ...

Physics and Python stuff. Most of the videos here are either adapted from class lectures or solving physics problems. I really like to use numerical calculations without all the fancy programming ...

1 Institute of Data Science and Engineering, Xuzhou University of Technology, Xuzhou, China 2 School of Mathematics and Statistics, Huaibei Normal University, Huaibei, China This study introduces a ...

Abstract: Maxwell's equations are transformed through discretisation of the solution domain using Finite Difference Method (FDM) to a system of algebraic equations referred to as finite difference ...

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 ...

Abstract: Partial differential equations (PDEs) are ubiquitous in physics and engineering and used for understanding various physical phenomena, including heat, diffusion, fluid and electrodynamics, ...

Proposed methods of removing toxic ‘forever chemicals’ from water have either only trapped the chemicals or broken them down. A new study has demonstrated a method that does both – quickly and cheaply ...

Euler Method: The simplest numerical method for solving ODEs, which uses the derivative to project forward. [ y_{n+1} = y_n + h \cdot f(x_n, y_n) ] Heun's Method (Improved Euler Method): A two-step ...