SOLUTION OF A PROBLEM FOR THE EQUATION OF OSCILLATION OF THE LONGITUDINALLY STRESSED ROD BY THE FINITE DIFFERENCE METHOD

Zakir F. Khankishiyev ()
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Zakir F. Khankishiyev: Department of Equations of Mathematical Physics, Baku State University, Baku, Azerbaijan

FRACTALS (fractals), 2025, vol. 33, issue 06, 1-12

Abstract: The paper considers a problem for the equation of oscillation of a longitudinally stressed rod, with boundary conditions containing partial derivatives of the desired function of high orders. It is known that when applying the finite difference method to solutions of problems for differential equations, difficulties arise in approximating the boundary conditions if they involve partial derivatives of the desired solution of high orders. Here, a method for constructing a difference problem that approximates the original problem with the second order of accuracy is given. A method for solving the constructed difference problem is investigated and an algorithm for solving this problem is given.

Keywords: Longitudinally Stressed Rod; Difference Problem; Stability; Approximation; Approximation Error; Fractional Models (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1142/S0218348X25401310

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