具有罗宾条件或附加质量条件的区间波方程的前后波剖面描述中的拉盖尔多项式

IF 0.6 4区数学 Q3 MATHEMATICS

Mathematical Notes Pub Date : 2024-07-15 DOI:10.1134/s0001434624050146

F. O. Naydyuk, V. L. Pryadiev, S. M. Sitnik

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引用次数: 0

摘要

摘要我们得到了一个描述区间上波方程初边界值问题解的前向和后向波形的公式。我们考虑了以下边界条件组合：(i) 在区间左端点的第一种条件和在右端点的第三种条件。 (ii) 左端点的第二种条件和右端点的第三种条件。 (iii) 左端点的第一种情况和右端点的附质量情况。 (iv) 左端点的第二类条件和右端点的附加质量条件。该公式包含有限多个算术运算、初等函数、二次函数以及初始数据独立参数的变换，如乘以一个数和取一个数的整数部分。

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Laguerre Polynomials in the Forward and Backward Wave Profile Description for the Wave Equation on an Interval with the Robin Condition or the Attached Mass Condition

Abstract

We obtain a formula describing the forward and backward wave profile for the solution of an initial–boundary value problem for the wave equation on an interval. The following combinations of boundary conditions are considered:

(i) The first-kind condition at the left endpoint of the interval and the third-kind condition at the right endpoint.

(ii) The second-kind condition at the left endpoint and the third-kind condition at the right endpoint.

(iii) The first-kind condition at the left endpoint and the attached mass condition at the right endpoint.

(iv) The second-kind condition at the left endpoint and the attached mass condition at the right endpoint.

The formula contains finitely many arithmetic operations, elementary functions, quadratures, and transformations of the independent argument of the initial data such as the multiplication by a number and taking the integer part of a number.

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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.