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Tari, Abolfazl,Shahmorad, Sedaghat The Korean Society for Computational and Applied M 2012 Journal of applied mathematics & informatics Vol.30 No.3
In this work, we investigate solving two-dimensional nonlinear Volterra integral equations of the first kind (2DNVIEF). Here we convert 2DNVIEF to the two-dimensional linear Volterra integral equations of the first kind (2DLVIEF) and then we solve it by using operational approach of the Tau method. But for solving the 2DLVIEF we convert it to an equivalent equation of the second kind and then by giving some theorems we formulate the operational Tau method with standard base for solving the equation of the second kind. Finally, some numerical examples are given to clarify the efficiency and accuracy of presented method.
Abolfazl Tari,Sedaghat Shahmorad 한국전산응용수학회 2012 Journal of applied mathematics & informatics Vol.30 No.3
In this work, we investigate solving two-dimensional nonlinear Volterra integral equations of the first kind (2DNVIEF). Here we convert 2DNVIEF to the two-dimensional linear Volterra integral equations of the first kind (2DLVIEF) and then we solve it by using operational approach of the Tau method. But for solving the 2DLVIEF we convert it to an equivalent equation of the second kind and then by giving some theorems we formulate the operational Tau method with standard base for solving the equation of the second kind. Finally, some numerical examples are given to clarify the efficiency and accuracy of presented method.
Numerical solution of a class of the Nonlinear Volterra Integro-Differential Equations
Leila Saeedi,Abolfazl Tari,Sayyed Hodjatollah Momeni Masuleh 한국전산응용수학회 2013 Journal of applied mathematics & informatics Vol.31 No.1
In this paper, we develop the operational Tau method for solving nonlinear Volterra integro-differential equations of the second kind. The existence and uniqueness of the problem is provided. Here, we show that the nonlinear system resulted from the operational Tau method has a semi triangular form, so it can be solved easily by the forward substitution method.\\Finally, the accuracy of the method is verified by presenting some numerical computations.