Shahed University
Two-step collocation methods for two-dimensional Volterra integral equations of the second kind
Abolfazl Tari Marzabad | S. M. Torabi | Sedaghat Shahmorad Moghanloo
URL :
http://research.shahed.ac.ir/WSR/WebPages/Report/PaperView.aspx?PaperID=116897
Date :
2019/05/14
Publish in :
Journal of Applied Analysis
Link :
https://www.degruyter.com/view/j/jaa
Keywords :
Abstract :
In this paper, we develop two-step collocation (2-SC) methods to solve two-dimensional nonlinear Volterra integral equations (2D-NVIEs) of the second kind. Here we convert a 2D-NVIE of the second kind to a one-dimensional case, and then we solve the resulting equation numerically by two-step collocation methods. We also study the convergence and stability analysis of the method. At the end, the accuracy and efficiency of the method is verified by solving two test equations which are stiff. In examples, we use the well-known differential transform method to obtain starting values.
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Abolfazl Tari Marzabad