Numerical simulation of a singularly perturbed fourth order equation by preliminary integration method
Keywords:
preliminary integration method, integration constants, algebraic system, high accuracy, efficiencyAbstract
In this article, the numerical simulation of a boundary value problem for a fourth order inhomogeneous differential equation with a small parameter at the highest deriva tive is carried out using the preliminary integration method. The numerical calculations performed show the high accuracy and efficiency of the method for various values of the small parameter and approximating Chebyshev polynomials of the first kind.
References
Ильин А.М.Разностнаясхемадлядифференциальногоуравнениясмалымпараметром при старшей производной. Матем. Заметка,– 1969, Т.6, вып. 2,– С. 237–248.
Бахвалов Н.С. К оптимизации методов решения краевых задач при наличии погранич ного слоя.–Ж.вычисл. матем. и матем.физ.,– 1969, Т.9, №4,– С. 841–859.
Лисейкин В.Д., Яненко Н.Н. Оравномерно сходящемся алгоритме численного решения обыкновенного дифференциального уравнения второго порядка с малым параметром при старшейпроизводной. Численные методымеханикисплошнойсреды. Новосибирск,– 1981. Т.12, №2,– С. 45–56.
Li J. Convergence analysis of finite element methods for singularly perturbed problems. Computers and Mathematics with Applications 40– 2000.– no. 6-7,– P. 735–745.
Jun-Sheng Duan, Li-Xia Jing, Ming Li. The mixed boundary value problems and Chebyshev Collocation Method for Caputo-Type fractional ordinary differential equations. Fractal Fract.– 2022. 6, 148. https://doi.org/10.3390/fractalfract6030148.
Абидуев П.Л., Дармаев Т.Г., Лисейкин В.Д. Численное решение сингулярно возмущен ных краевых задач 4-го порядка. Вестник БГУ. Математика, информатика,– 2022. 4:– P. 3–11.
Liseikin V.D. Survey of Layer Structures and coordinate Transformations Eliminating Layers world Journal of physics,– 2024. 2(1),– P. 143–171.
Normurodov Ch.B., Tursunova B.A. Numerical modeling of the boundary value problem of an ordinary differential equation with a small parameter at the highest derivative by Chebyshev polynomials of the second kind. Results in Applied mathematics.– 2023. (1):1 6.DOI: https://doi.org/10.1016/j.rinam.2023.100388
Abutaliev F.B., Narmuradov Ch.B. Mathematical modeling of the problem of hydrodynamic stability. Tashkent:Fan va texnologiya:– 2011. 188.
Nоrmuratov Ch.B. Solving the Orr-Sommerfeld equation using the spectral grid method. Dokl.AN RUz.– 2001. (10-11):– P. 9–12.
Nоrmuratov Ch.B. About one effective method for solving the Orr-Sommerfeld equation. Math modeling.– 2005. 9(17):– P. 35–42.
Nоrmuratov Ch.B. Mathematical modeling of hydrodynamic problems for two-phase plane parallel flows. Math modeling.– 2007. 6(19):– P. 53–60.
Normurodov Ch.B., Toyirov A.Kh., Ziyakulova Sh.A., Visvanathan K.K. Convergence of Spectral-Grid Method for Byurgers equation with initial-boundary conditions. Mathematics and Statistics.2024;12(2):115-125.DOI:10.13189/ms.2024.120201.Avialable at :http://www.hrpub.org
Normurodov Ch.B., Abdurakhimov B.F., Viswanathan K.K., Saravanan D., Djurayeva N.T. Application of numerical simulation of two-phase hydrodynamic flows. European chemical bulletin.– 2023.– P. 959–968.
											