Finite Difference Schemes: A Comprehensive Overview

Authors

  • Turganbaeva Ramiza Tolibaevna A student of the Faculty of Mathematics of KSU
  • Qa’llibekov U’mitbek O’serbay uli A student of the Faculty of Mathematics of KSU
  • Abatbaev Rasulbek Nietbay uli A student of the Faculty of Mathematics of KSU
  • Mnajatdinov Atabek Rafatdin uli A student of the Faculty of Mathematics of KSU

Keywords:

Finite difference schemes, numerical analysis, differential equations, mathematics, informatics, partial differential equations

Abstract

Finite difference schemes are fundamental numerical methods used in mathematics and informatics for solving differential equations and modeling various physical and computational phenomena. This article provides a comprehensive overview of finite difference schemes, discussing their principles, applications, advantages, and limitations. We delve into the mathematical foundations, explore different types of finite difference approximations, and highlight their significance in solving partial and ordinary differential equations. Furthermore, we examine their role in informatics, including their applications in computer graphics, image processing, and computational fluid dynamics. This article aims to offer readers a thorough understanding of finite difference schemes and their widespread implications across diverse scientific and technological domains.

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Published

2023-08-22