Two-dimensional triangular functions and their applications to nonlinear 2D Volterra–Fredholm integral equations

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• 作者：E. Babolian ; K. Maleknejad ; M. Roodaki ; H. Almasieh
• 关键词：Two-dimensional orthogonal triangular functions ; Nonlinear Volterra– ; Fredholm integral equations ; Direct method ; Operational matrix
• 刊名：Computers and Mathematics with Applications
• 出版年：2010
• 出版时间：September 2010
• 年：2010
• 卷：60
• 期：6
• 页码：1711-1722
• 全文大小：368 K

文摘

Two-dimensional orthogonal triangular functions (2D-TFs) are presented as a new set of basis functions for expanding 2D functions. Their properties are determined and an operational matrix for integration obtained. Furthermore, 2D-TFs are used to approximate solutions of nonlinear two-dimensional integral equations by a direct method. Since this approach does not need integration, all calculations can be easily implemented, and several advantages in reducing computational burdens arise. Finally, the efficiency of this method will be shown by comparison with some numerical results.