DOI: 10.12732/ijam.v38i4.1
ON ONE HIGHLY ACCURATE AND
EFFICIENT METHOD FOR SOLVING
THE BIHARMONIC EQUATION
Chori Begaliyevich Normurodov1,*, Shakhnoza Abdirasulovna Ziyakulova1, Sardorbek Komil o'g'li Murodov1
1Termez State University, 190111, 43 Barkamol Avlod Street, Termiz, UZBEKISTAN
Abstract. In this paper, a discrete version of the preliminary integration method for the numerical solution of the boundary value problem of a non-homogeneous biharmonic equation is proposed. Partial derivatives of the equation are presented in the form of finite double series in Chebyshev polynomials of the first kind with unknown expansion coefficients. Using discrete integration formulas that reduce the order of derivatives, the main equation is "integrated" four times both with respect to the variable "x" and the variable "y". By adding boundary conditions written in the form of finite double series to the resulting equation, an algebraic system is formed for determining the unknown coefficients. The numerical calculations performed with the selected various trial functions show the high accuracy and efficiency of the proposed method.
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DOI: 10.12732/ijam.v38i4.1
Source: International Journal of Applied Mathematics
ISSN printed version: 1311-1728
ISSN on-line version: 1314-8060
Year: 2025
Volume: 38
Issue: 4
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