带分数阶幂椭圆算子的双曲型Volterra积分微分方程谱方法的正则化

IF 2.4 Q2 ENGINEERING, MECHANICAL Nonlinear Engineering - Modeling and Application Pub Date : 2023-01-01 DOI:10.1515/nleng-2022-0250
F. Mirzaei G., D. Rostamy
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引用次数: 0

摘要

摘要本文提出了求解线性和非线性双曲型Volterra积分微分方程(HVIDEs)的数值方法。将正则化的legende -搭配谱法应用于求解第二类HVIDE,时间变量和空间变量分别基于legende - gauss - lobatto和legende - gauss (LG)插值点。对于有界域,将给定的HVIDE关系转换为三个对应的关系。因此,采用legende -配置谱法求解该方程,得到了病态线性方程组和病态非线性方程组;因此,使用不同的正则化方法来求解它们。对于无界域,使用合适的映射将问题转换到有界域上,然后将相同的方法应用于有界域。对于这两种情况,数值结果证实了指数收敛速度。本研究的结果对于双曲型积分微分方程的谱方法的正则化是前所未有的。这项工作的结果似乎是双曲型积分微分方程的谱方法正则化的第一次成功。
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The regularization of spectral methods for hyperbolic Volterra integrodifferential equations with fractional power elliptic operator
Abstract In this study, a numerical approach is presented to solve the linear and nonlinear hyperbolic Volterra integrodifferential equations (HVIDEs). The regularization of a Legendre-collocation spectral method is applied for solving HVIDE of the second kind, with the time and space variables on the basis of Legendre-Gauss-Lobatto and Legendre-Gauss (LG) interpolation points, respectively. Concerning bounded domains, the provided HVIDE relation is transformed into three corresponding relations. Hence, a Legendre-collocation spectral approach is applied for solving this equation, and finally, ill-posed linear and nonlinear systems of algebraic equations are obtained; therefore different regularization methods are used to solve them. For an unbounded domain, a suitable mapping to convert the problem on a bounded domain is used and then apply the same proposed method for the bounded domain. For the two cases, the numerical results confirm the exponential convergence rate. The findings of this study are unprecedented for the regularization of the spectral method for the hyperbolic integrodifferential equation. The result in this work seems to be the first successful for the regularization of spectral method for the hyperbolic integrodifferential equation.
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来源期刊
CiteScore
6.20
自引率
3.60%
发文量
49
审稿时长
44 weeks
期刊介绍: The Journal of Nonlinear Engineering aims to be a platform for sharing original research results in theoretical, experimental, practical, and applied nonlinear phenomena within engineering. It serves as a forum to exchange ideas and applications of nonlinear problems across various engineering disciplines. Articles are considered for publication if they explore nonlinearities in engineering systems, offering realistic mathematical modeling, utilizing nonlinearity for new designs, stabilizing systems, understanding system behavior through nonlinearity, optimizing systems based on nonlinear interactions, and developing algorithms to harness and leverage nonlinear elements.
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