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

✍ Scribed by E. Babolian; K. Maleknejad; M. Roodaki; H. Almasieh

Publisher
Elsevier Science
Year
2010
Tongue
English
Weight
369 KB
Volume
60
Category
Article
ISSN
0898-1221

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✦ Synopsis

a b s t r a c t 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.

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✍ K. Maleknejad; K. Mahdiani 📂 Article 📅 2011 🏛 Elsevier Science 🌐 English ⚖ 265 KB

## a b s t r a c t Few numerical methods such as projection methods, time collocation method, trapezoidal Nystrom method, Adomian decomposition method and some else are used for mixed Volterra-Fredholm integral equations. The main purpose of this paper is to use the piecewise constant two-dimensio