This article examines numerical methods for solving boundary value problems for parabolic differential equations, which are widely used in modeling physical processes such as the filtration of oil, gas, and water in porous media, as well as heat transfer processes.The primary focus is on the differentialdifference method, which is characterized by its high accuracy and ease of programming.The theoretical aspects of the method are presented, including algorithmic implementation, the use of the differential sweep method, and an analysis of the stability of the computational process.Special attention is given to the advantages of the differential-difference approach, such as the ability to automatically fulfill internal conditions during phase transitions, ensure absolute computational stability, and simplify programming.The article also describes the solution algorithm, which includes a longitudinal-transverse scheme that enables efficient problem-solving using parallel computations.Additionally, numerical calculation results are provided, including comparisons with analytical solutions that demonstrate the method's high accuracy.It is shown that the developed algorithms can be easily adapted for solving other classes of problems, making them a universal tool for numerical modeling in computational mathematics.The conclusions are supported by graphical results and error analysis, confirming the reliability of the proposed approach.
| Jurnal | ТАТУ хабарлари |
|---|---|
| Nashriyot | Тошкент ахборот технологиялари университети |
| ISSN | 2010-9857, 2181-1083 |
| Nashr sanasi | 2024-12-29 |
| Til | Ingliz |
| Ilmiy soha | Texnika |
| DOI | 10.61663/244tuitmct3 |
| Indeksga qo‘shilgan | 2026-09-02 |
DOI: 10.61663/244tuitmct3 · Maqolaning asl sahifasi
| APA | Noma’lum muallif (2024). Numerical Modeling Of Boundary Value Problems For Parabolic Differential Equations. ТАТУ хабарлари. https://doi.org/10.61663/244tuitmct3 |
|---|---|
| GOST (OAK) | Noma’lum muallif Numerical Modeling Of Boundary Value Problems For Parabolic Differential Equations // ТАТУ хабарлари. – 2024. – DOI: 10.61663/244tuitmct3. |
| MLA | Noma’lum muallif. “Numerical Modeling Of Boundary Value Problems For Parabolic Differential Equations.” ТАТУ хабарлари, 2024. https://doi.org/10.61663/244tuitmct3 |
| Chicago | Noma’lum muallif. “Numerical Modeling Of Boundary Value Problems For Parabolic Differential Equations.” ТАТУ хабарлари (2024). https://doi.org/10.61663/244tuitmct3 |
| Harvard | Noma’lum muallif (2024) ‘Numerical Modeling Of Boundary Value Problems For Parabolic Differential Equations’, ТАТУ хабарлари. https://doi.org/10.61663/244tuitmct3 |
| BibTeX | @article{article2024,
title = {Numerical Modeling Of Boundary Value Problems For Parabolic Differential Equations},
author = {Unknown},
journal = {ТАТУ хабарлари},
year = {2024},
doi = {10.61663/244tuitmct3},
url = {https://doi.org/10.61663/244tuitmct3}
} |
Boshqa maqola uchun iqtibos tayyorlash
The purpose of the work in this article is to develop models and algorithms to ensure the effectiveness of monitoring the telecommunications network of information transmission in air navigation systems, allowing to…
Algorithm and software for calculating
The purpose of this article is to study the main approaches and algorithms for building recommendation services in online trading systems.Recommendation systems optimize the sales process by identifying interesting and…
Abctract -The article studies the issues of information support for solving functionalissues of automated management of corporate information exchange (on the example of tax authorities), the design of its control…
The paper considers the issue of improving the mathematical model for a hybrid method of machine translation evaluation.Today, electronic translation remains a popular tool.The development of technologies and adaptation…
In this work, numerical processing of signals using high-order spline models in the direction of the approximation theory of mathematical modeling, which plays an important role in the development of science, is…
This paper presents a comprehensive study of defuzzification methods designed specifically for intuitionistic fuzzy sets (IFS), which extend traditional fuzzy sets by incorporating an additional dimension of…
After many scientific studies in the world, we can say that the use of spline functions in working with digital signals is widely used and good results are achieved.Nowadays, there are many ways to wish digital…
This study investigates the gas motion through the froth of a prototype bidimensional flotation cell.Using advanced video and image analysis techniques, surface velocity data obtained with a Visiofroth system were…
ТАТУ хабарлари — barcha maqolalar · 2024-yil arxivi
This article examines compression as a meaning-oriented strategy in sign language translation and interpreting. Compression is understood not as arbitrary shortening, but as the selective reformulation of a source…
This study investigates the impact of Edge Computing on bandwidth utilization in Internet of Things (IoT)–driven Nigerian telecom networks. The rapid growth of IoT devices has significantly increased data traffic…
This article analyzes the scientific, pedagogical, and methodological foundations for the effective integration of national upbringing factors with modern global competencies in the context of continuous education…
This article addresses the problem of improving an adaptive traffic signal control algorithm at urban intersections by taking into account the dynamic characteristics of traffic flow. Fixed-time control under conditions…
Maqolada paxta xomashyosini yirik iflosliklardan tozalash jarayonida arrali baraban va kolosnikli panjara o‘rtasidagi o‘zaro ta’sirni takomillashtirish masalasi ko‘rib chiqilgan. Mavjud tozalagichlarda qo‘llaniladigan…
Maqolada paxta xomashyosini yirik va mayda iflosliklardan tozalash samaradorligini oshirishga qaratilgan ilmiy tadqiqotlar tizimlashtirilib, konstruktiv va texnologik omillarning o‘zaro ta’siri qiyosiy tahlil qilindi…