Hybrid-Galerkin Approach for Solving Two-dimensional Volterra-Fredholm Integral Equations
Journal Title: Journal of Science and today’s world - Year 2017, Vol 6, Issue 12
Abstract
The main focus of this paper is to present an effective numerical method for solving two-dimensional Volterra-Fredholm integral equations, which occur in modeling of many phenomena in physics and engineering. For this purpose, we provide a novelty set of two-dimensional basis functions by combination of bivariate Legendre polynomials and block-pulse functions. We entitle them "2D-LHFs". In our method, we use the exact forms of the known functions in integral equation. So, in comparison of other similar methods, we achieve to a more accurate solution. The proposed method reduces an integral equation to a system of algebraic equations. Moreover, some theorems about the convergence and error of 2D-LHFs are proved. We present some examples and compare our numerical results with the other methods ones, to confirm the efficiency and accuracy of the proposed method.
Authors and Affiliations
M. Roodaki , Z. JafariBehbahani
Keywords
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