首页|Nystr?m Method to Solve Two-Dimensional Volterra Integral Equation with Discontinuous Kernel
Nystr?m Method to Solve Two-Dimensional Volterra Integral Equation with Discontinuous Kernel
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In this paper, a linear two-dimensional Volterra integral equation of the second kind with the discontinuous kernel is considered. The conditions for ensuring the existence of a unique continuous solution are mentioned. The product Nystr?m method, as a well-known method of solving singular integral equations, is presented. Therefore, the Nystr?m method is applied to the linear Volterra integral equation with the discontinuous kernel to convert it to a linear algebraic system. Some formulas are expanded in two dimensions. Weights' functions of the Nystr?m method are obtained for kernels of logarithmic and Carleman types. Some numerical applications are presented to show the efficiency and accuracy of the proposed method. Maple18 is used to compute numerical solutions. The estimated error is calculated in each case. The Nystr?m method is useful and effective in treating the two-dimensional singular Volterra integral equation. Finally, we conclude that the time factor and the parameter v have a clear effect on the results.
Volterra Integral EquationTwo-Dimensional Volterra Integral EquationsNystr?m Method.
Sameeha Ali Raad、Mariam Mohammed Al-Atawi
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Department of Mathematical Sciences, College of Applied Sciences, Umm Al-Qura University, 21955, Saudi Arabia
Mathematics Department, College of Applied Sciences, University of Tabuk, 71411, Saudi Arabia
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