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, ...

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: This letter proposes a generalized and controllable-stability conformal method to address stability challenges inherent in conformal finite-difference time-domain algorithms. A quantitative ...

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 ...

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 ...

Abstract: Estimating stochastic gradients is pivotal in fields like service systems in operations research. The classical method for this estimation is the finite-difference approximation, which ...

The research findings have demonstrated that finite difference methods offer a powerful tool for approximating option prices and hedging parameters, especially in cases where closed-form solutions are ...

This package provides a set of functions to create and solve discretization problems associated with finite difference methods on nonuniform grids.

Introduction: Fractional diffusion equations offer an effective means of describing transport phenomena exhibiting abnormal diffusion pat-terns, often eluding traditional diffusion models. Methods: We ...