Numerical Algorithms for Solving One Type of Singular Integro-Differential Equation Containing Derivatives of the Time Delay States

Autor:	Terry L. Herdman, Shihchung Chiang
Rok vydání:	2015
Předmět:	Differential equation Singular solution Integro-differential equation Mathematical analysis Convergence (routing) Order of accuracy General Medicine Aeroelasticity Algorithm Numerical stability Mathematics Equation solving
Zdroj:	Applied Mathematics. :1294-1301
ISSN:	2152-7393 2152-7385
DOI:	10.4236/am.2015.68123
Popis:	This study presents numerical algorithms for solving a class of equations that partly consists of derivatives of the unknown state at previous certain times, as well as an integro-differential term containing a weakly singular kernel. These equations are types of integro-differential equation of the second kind and were originally obtained from an aeroelasticity problem. One of the main contributions of this study is to propose numerical algorithms that do not involve transforming the original equation into the corresponding Volterra equation, but still enable the numerical solution of the original equation to be determined. The feasibility of the proposed numerical algorithm is demonstrated by applying examples in measuring the maximum errors with exact solutions at every computed nodes and calculating the corresponding numerical rates of convergence thereafter.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::4ca5b1ccba75185c66aa2d100c4c7b51 https://doi.org/10.4236/am.2015.68123 Zobrazit plný text záznamu