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.
Katani, R., & Shahmorad, S. (2013). A new block by block method for solving two-dimensional linear
and nonlinear Volterra integral equations of the first and second kinds. Bulletin of the Iranian Mathematical Society, 39(4), 707-724.
MLA
R. Katani; S. Shahmorad. "A new block by block method for solving two-dimensional linear
and nonlinear Volterra integral equations of the first and second kinds". Bulletin of the Iranian Mathematical Society, 39, 4, 2013, 707-724.
HARVARD
Katani, R., Shahmorad, S. (2013). 'A new block by block method for solving two-dimensional linear
and nonlinear Volterra integral equations of the first and second kinds', Bulletin of the Iranian Mathematical Society, 39(4), pp. 707-724.
VANCOUVER
Katani, R., Shahmorad, S. A new block by block method for solving two-dimensional linear
and nonlinear Volterra integral equations of the first and second kinds. Bulletin of the Iranian Mathematical Society, 2013; 39(4): 707-724.
)