Numerical solution of the linear two-dimensional Fredholm integral equations of the second kind via two-dimensional triangular orthogonal functions

Farshid Mirzaee; Sima Piroozfar

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Numerical solution of the linear two-dimensional Fredholm integral equations of the second kind via two-dimensional triangular orthogonal functions

机译：第二类线性二维弗雷德霍尔姆积分方程的二维三角正交函数数值解

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In this paper, we will give some results for developing the two-dimensional triangular orthogonal functions (2D-TFs) for numerical solution of the linear two-dimensional Fredholm integral equations of the second kind. The product of 2D-TFs and some formulas for calculating definite integral of them are derived and utilized to reduce the solution of two-dimensional Fredholm integral equation to the solution of algebraic equations. Also a theorem is proved for convergence analysis. Numerical examples are presented and results are compared with analytical solution to demonstrate the validity and applicability the method.

机译：在本文中，我们将提供一些结果，用于开发第二类线性二维Fredholm积分方程数值解的二维三角正交函数（2D-TFs）。推导了2D-TFs的乘积和一些计算它们的确定积分的公式，并将其用于将二维Fredholm积分方程的解简化为代数方程的解。还证明了一个定理用于收敛性分析。数值算例与分析结果进行了比较，证明了该方法的有效性和适用性。

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《Journal of King Saud University》 |2010年第4期|共9页
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Farshid Mirzaee; Sima Piroozfar;
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中图分类自然科学理论与方法论;
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7. Numerical solution of the linear two-dimensional Fredholm integral equations of the second kind via two-dimensional triangular orthogonal functions [O] . Mirzaee Farshid, Piroozfar Sima 2010

机译：第二类线性二维弗雷德霍尔姆积分方程的二维三角正交函数数值解

Numerical solution of the linear two-dimensional Fredholm integral equations of the second kind via two-dimensional triangular orthogonal functions

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