Solving generalized pantograph equations by shifted orthonormal Bernstein polynomials

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• 作者：Shahnam Javadi ; Esmail Babolian ; Zeinab Taheri ; ^{zeinabtaheritari@gmail.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Shifted orthonormal Bernstein polynomials (SOBPs) ; Operational matrices ; Pantograph equations ; Condition numbers ; Error analysis
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2016
• 出版时间：September 2016
• 年：2016
• 卷：303
• 期：Complete
• 页码：1-14
• 全文大小：431 K

文摘

In this paper, we introduce Shifted Orthonormal Bernstein Polynomials (SOBPs) and derive the operational matrices of integration and delays for these polynomials. Then, we apply them to convert the pantograph equations to a system of linear equations. An important property of this method is that the condition number of the coefficient matrix of the system is small which confirms that our method is stable. Error analysis and comparison with other methods are given to confirm the validity, efficiency and applicability of the proposed method.