On Rational Spline Solutions of Differential Equations with Singularities in the Coefficients of the Derivatives

IF 0.6 4区数学 Q3 MATHEMATICS

Mathematical Notes Pub Date : 2024-04-22 DOI:10.1134/s0001434624010061

V. G. Magomedova, A.-R. K. Ramazanov

引用次数: 0

Abstract

For one generalization of the Riemann differential equation, we obtain sufficient conditions for the approximability by twice continuously differentiable rational interpolation spline functions. To solve the corresponding boundary value problem numerically, a tridiagonal system of linear algebraic equations is constructed and conditions on the coefficients of the differential equation are found guaranteeing the uniqueness of the solution of such Estimates of the deviation of the discrete solution of the boundary value problem from the exact solution on a grid are presented.

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论微分方程的有理样条解法与微分系数的奇异性

摘要对于黎曼微分方程的一种概化，我们获得了用两次连续可微的有理插值样条函数逼近的充分条件。为了数值求解相应的边界值问题，我们构造了一个三对角线线性代数方程组，并找到了微分方程系数的条件，以保证该方程组解的唯一性估算了边界值问题离散解与网格上精确解的偏差。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Mathematical Notes 数学-数学

CiteScore

0.90

自引率

16.70%

发文量

179

审稿时长

24 months

期刊介绍： Mathematical Notes is a journal that publishes research papers and review articles in modern algebra, geometry and number theory, functional analysis, logic, set and measure theory, topology, probability and stochastics, differential and noncommutative geometry, operator and group theory, asymptotic and approximation methods, mathematical finance, linear and nonlinear equations, ergodic and spectral theory, operator algebras, and other related theoretical fields. It also presents rigorous results in mathematical physics.