A NEW BLOCK BY BLOCK METHOD FOR SOLVING TWO-DIMENSIONAL LINEAR AND NONLINEAR VOLTERRA INTEGRAL EQUATIONS OF THE FIRST AND SECOND KINDS

作者：Katani R; Shahmorad S^*

来源：Bulletin of the Iranian Mathematical Society, 2013, 39(4): 707-724.

• Two-dimensional Volterra integral equations
• Romberg quadrature rule
• block by block method
• Gronwall inequality

In this paper, we propose a new method for the numerical solution of two-dimensional linear and nonlinear Volterra integral equations of the first and second kinds, which avoids from using starting values. An existence and uniqueness theorem is proved and convergence is verified by using an appropriate variety of the Gronwall inequality. Application of the method is demonstrated for solving the useful telegraph equation.

• 出版日期2013-9