APPROXIMATE SOLUTION OF BOUNDARY VALUE PROBLEMS TO SIMPLE DIFFERENTIAL EQUATIONS
https://doi.org/10.5281/zenodo.15266139
Keywords:
boundary value problem, differential equation, boundary conditions, first, second, third kind, basic functions, least squares method, approximate solution, linear system, difference, approximationAbstract
This article discusses a general approach to solving second-order boundary value problems with two boundary conditions of various types (first, second, and third kind) using approximate analytical methods. Special attention is paid to the construction of basic functions satisfying specified boundary conditions and the application of the integral least squares method to find an approximate solution. It shows how to choose linear and one-parameter forms of basic functions, as well as how to create a linear system for determining the expansion coefficients. As an illustration, an example with an exact solution and its approximate analogue is given. The technique emphasizes the importance of choosing the right basic functions to improve the accuracy of the approximation.
Downloads
References
Nuraliyev T. et al. MATRISANING XOS SON VA XOS VEKTORLARNI TOPISH //Science technology&Digital finance. – 2024. – Т. 2. – №. 4. – С. 62-71.
Nuraliyev T. A. et al. ODDIY DIFFERENSIAL TENGLAMALAR UCHUN CHEGARAVIY MASALALARNI YECHISHNING TAQRIBIY-ANALITIK USULI: GALYORKIN USULI //International Journal of scientific and Applied Research. – 2024. – Т. 1. – №. 3. – С. 312-315.
Рустамов М., Нуралиев Т. Giperbolik tenglamalarda kuzatish masalasi matematik modeli tadqiqi //Новый Узбекистан: наука, образование и инновации. – 2024. – Т. 1. – №. 1. – С. 72-74.
Рустамов М., Нуралиев Т. Задача наблюдения в уравнении гиперболического типа //Информатика и инженерные технологии. – 2023. – Т. 1. – №. 1. – С. 132-133.
Нуралиев Т. Issiqlik o ‘tkazuvchanlik tenglamasi uchun ayirmali sxemalar //Информатика и инженерные технологии. – 2023. – Т. 1. – №. 2. – С. 193-197.
Alimardanovich N. T. CHIZIQSIZ TENGLAMALARNI TAQRIBIY YECHISH //International Journal of Contemporary Scientific and Technical Research. – 2022. – С. 323-327.
Alimardanovich N. T. et al. CHIZIQLI ALGEBRAIK TENGLAMALAR TIZIMINI ECHISH. ITERATSION USULLAR //ОБРАЗОВАНИЕ НАУКА И ИННОВАЦИОННЫЕ ИДЕИ В МИРЕ. – 2023. – Т. 20. – №. 1. – С. 153-159.
Alimardanovich N. T. et al. ZEYDEL USULI //ОБРАЗОВАНИЕ НАУКА И ИННОВАЦИОННЫЕ ИДЕИ В МИРЕ. – 2023. – Т. 20. – №. 1. – С. 169-176.
Alimardanovich N. T. et al. ODDIY ITERATSION USUL //ОБРАЗОВАНИЕ НАУКА И ИННОВАЦИОННЫЕ ИДЕИ В МИРЕ. – 2023. – Т. 20. – №. 1. – С. 160-168.
Nuraliyev T., Xandamov Y. Оddiy differensial tenglamalarni sonli yechish //Zamonaviy innovatsion tadqiqotlarning dolzarb muammolari va rivojlanish tendensiyalari: yechimlar va istiqbollar. – 2022. – Т. 1. – №. 1. – С. 347-349.
Alimardanovich N. T., Abduqodirovich N. N. PLASTINKA UCHUN IKKI O’LCHOVLI ISSIQLIK O’TKAZUVCHANLIK TENGLAMASINI SONLI YECHISH //ОБРАЗОВАНИЕ НАУКА И ИННОВАЦИОННЫЕ ИДЕИ В МИРЕ. – 2023. – Т. 15. – №. 3. – С. 141-143.
Xandamov Y. Nuraliyev T. Teng qadamlar uchun nyutonning 1-interpolyatsion formulasi uchun algoritm va dasturiy ta ‘minot yaratish //Zamonaviy innovatsion tadqiqotlarning dolzarb muammolari va rivojlanish tendensiyalari: yechimlar va istiqbollar. – 2022. – Т. 1. – №. 1. – С. 364-367.
Агабаев Д. Х. и др. ИНТЕРПОЛЯЦИОННАЯ ФОРМУЛА ЛАГРАНЖА //ЛУЧШИЕ НАУЧНЫЕ ИССЛЕДОВАНИЯ 2024: сборник статей XV. – 2024. – С. 9.
Toʻlqin N. HOSIL BOʻLADIGAN XATOLIKLARNI BAHOLASH //International Journal of Contemporary Scientific and Technical Research. – 2023. – С. 359-363.
Baxtiyor P. et al. BA’ZI BIR MUHIM XOSMAS INTEGRALLARNI HISOBLASHDA FRULLANI FORMULASIDAN FOYDALANISH //International Journal of Contemporary Scientific and Technical Research. – 2023. – С. 363-367.
Po‘latov B., Ibrohimov J. BA’ZI RATSIONAL FUNKSIYALARNI INTEGRALLASHDA OSTRAGRADSKIY USULIDAN FOYDALANISH //Talqin va tadqiqotlar. – 2023. – Т. 1. – С. 21.
Bahrom o‘g‘li I. J. OCHIQ CHIZIQLI QAVARIQ TO ‘PLAMDA POLINOMIAL QAVARIQLIKNING YETARLI SHARTI //International Journal of Contemporary Scientific and Technical Research. – 2022. – Т. 1. – №. 2. – С. 363-5.
Xurramov Y., Polatov B., Ibrohimov J. Kophadning keltirilmaslik alomati //Zamonaviy innovatsion tadqiqotlarning dolzarb muammolari va rivojlanish tendensiyalari: yechimlar va istiqbollar. – 2022. – Т. 1. – №. 1. – С. 399-401.
Xurramov Y., Polatov B., Ibrohimov J. Kophadning keltirilmaslik alomati //Zamonaviy innovatsion tadqiqotlarning dolzarb muammolari va rivojlanish tendensiyalari: yechimlar va istiqbollar. – 2022. – Т. 1. – №. 1. – С. 399-401.
Пулатов Б. и др. Darajali geometriyaning oddiy differensial tenglamalarda qo ‘llanilishi //Информатика и инженерные технологии. – 2023. – Т. 1. – №. 2. – С. 266-269.
Полатов Б., Хуррамов Ё., Иброхимов Д. Matematika darslarida muammoli oqitish texnologiyasidan foydalanish //Современные инновационные исследования актуальные проблемы и развитие тенденции: решения и перспективы. – 2022. – Т. 1. – №. 1. – С. 401-404.
Javohir I. et al. XEVISAYD USULI YORDAMIDA RATSIONAL FUNKSIYALARNI INTEGRALLASH //International Journal of Contemporary Scientific and Technical Research. – 2023. – Т. 416. – С. 418.
Polatov B., Xurramov Y., Ibrohimov J. Murakkab funksiyalardan olingan aniq integralni taqribiy hisoblash //Zamonaviy innovatsion tadqiqotlarning dolzarb muammolari va rivojlanish tendensiyalari: yechimlar va istiqbollar. – 2022. – Т. 1. – №. 1.
Javohir I. B.. o ‘g ‘li, & Muxammadiyev, GJ. o ‘g ‘li.(2023). AYRIM IRRATSIONAL KO ‘RINISHDAGI INTEGRALLARNI EYLER ALMASHTIRISHLARI YORDAMIDA RATSIONALLASHTIRISH //Educational Research in Universal Sciences. – Т. 2. – №. 2. – С. 237-241.
Бозоров А. Р. и др. ИНТЕГРИРОВАНИЕ РАЦИОНАЛЬНЫХ ФУНКЦИЙ ПО СХЕМЕ ГОРНЕРА //ДОСТИЖЕНИЯ ВУЗОВСКОЙ НАУКИ. – 2023. – Т. 2023. – С. 13-16.
Sobirovich P. B. Darajali Geometriyani Algebraik Tenglamalarda Qo ‘Llab Asimptotik Yechimlarini Topish. – 2022.
Nuraliyev T. et al. MATRISANING XOS SON VA XOS VEKTORLARNI TOPISH //Science technology&Digital finance. – 2024. – Т. 2. – №. 4. – С. 62-71.
САФАРОВА Ф. и др. РАЦИОНАЛИЗАЦИЯ НЕКОТОРЫХ ИНТЕГРАЛОВ ИРРАЦИОНАЛЬНОЙ ФОРМЫ С ПОМОЩЬЮ ЗАМЕН ЭЙЛЕРА. – Наука и Просвещение (ИП Гуляев ГЮ) КОНФЕРЕНЦИЯ: СТУДЕНТ ГОДА 2024 Пенза, 05 апреля 2024 года Организаторы: Наука и Просвещение (ИП Гуляев ГЮ), 2024.
Downloads
Published
Issue
Section
License
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
