References
- J. Abdalkhani. A numerical approach to the solution of Abel integral equations of the second kind with nonsmooth solution. Journal of Computational and Applied Mathematics, 29(3):249–255, 1990. http://dx.doi.org/10.1016/0377-0427(90)90011-N.
- A. Akyüz-Daşcioǧlu. Chebyshev polynomial solutions of systems of linear integral equations. Applied Mathematics and Computation, 151(1):221–232, 2004. http://dx.doi.org/10.1016/S0096-3003(03)00334-5.
- J. Biazar, E. Babolian and R. Islam. Solution of a system of Volterra integral equations of the first kind by Adomian method. Applied Mathematics and Computation, 139(2–3):249–258, 2003. http://dx.doi.org/10.1016/S0096-3003(02)00173-X.
- H. Brunner. The numerical solution of integral equations with weakly singular kernels. Num. Anal., 1066:50–71, 1984. http://dx.doi.org/10.1007/BFb0099518.
- H. Brunner and H.J.J.te Riele. Volterra-type integral equations of the second kind with nonsmooth solutions. Integral Equations, 6:187–203, 1984.
- K. Diethelm, J.M. Ford, N.J. Ford and M. Weilbeer. Pitfalls in fast numerical solvers for fractional differential equations. Journal of Computational and Applied Mathematics, 186(2):482–503, 2006. http://dx.doi.org/10.1016/j.cam.2005.03.023.
- M.T. Giraudo and L. Sacerdote. First entrance time distribution millimolarity in a model neuron. Quaderni di Dipartimento di Mathematica Universitá di Torino, 18, 2002.
- A. Golbabai, M. Mammadov and S. Seifollahi. Solving a system of nonlinear integral equations by an RBF network. Computer & Mathematics with Applications, 57(10):1651–1658, 2009. http://dx.doi.org/10.1016/j.camwa.2009.03.038.
- R. Gorenflo and S. Vessella. Abel Integral Equations: Analysis and Applications. Springer, Berlin, 1991. http://dx.doi.org/10.1007/BFb0084665.
- B. Jumarhon and S. Mckee. On the heat equation with nonlinear and nonlocal boundary conditions. Journal of Mathematical Analysis and Applications, 190:806–820, 1995. http://dx.doi.org/10.1006/jmaa.1995.1113.
- R. Katani and S. Shahmorad. Block by block method for the systems of nonlinear Volterra integral equations. Applied Mathematical Modelling, 34:400–406, 2010. http://dx.doi.org/10.1016/j.apm.2009.04.013.
- K. Maleknejad and M. Shahrezaee. Using Runge-Kutta method for numerical solution of the system of Volterra integral equation. Appl. Math. and Comp., 149(2):399–410, 2004. http://dx.doi.org/10.1016/S0096-3003(03)00148-6.
- K. Maleknejad and A. Salimi Shamloo. Numerical solution of singular Volterra integral equations system of convolution type by using operational matrices. Applied Mathematics and Computation, 195(2):500–505, 2008. http://dx.doi.org/10.1016/j.amc.2007.05.001.
- S. McKee, T. Tang and T. Diogo. An Euler-type method for two-dimensional Volterra integral equations of the first kind. IMA Journal of Numerical Analysis, 20(3):423–440, 2000. http://dx.doi.org/10.1093/imanum/20.3.423.
- R. Metzler and J. Klafter. The random walk's guide to anomalous diffusion: a fractional dynamics approach. Physics Reports, 339(1):1–77, 2000. http://dx.doi.org/10.1016/S0370-1573(00)00070-3.
- M. Rabbani, K. Maleknejad and N. Aghazadeh. Numerical computational solution of the Volterra integral equations system of the second kind by using an expansion method. Applied Mathematics and Computation, 187(2):1143–1146, 2007. http://dx.doi.org/10.1016/j.amc.2006.09.012.
- L. Tao and H. Yong. Extrapolation method for solving weakly singular nonlinear Volterra integral equations of the second kind. Journal of Mathematical Analysis and Applications, 324(1):225–237, 2006. http://dx.doi.org/10.1016/j.jmaa.2005.12.013.
- M. E. A. El Tom. Application of spline functions to system of Volterra integral equation of the first and second kinds. IMA, Appl. Math., 17(3):295–310, 1976.
- A. Young. The application of approximate product-integration to the numerical solution of integral equations. Proceeding of Royal Society of London. Series A, 224:561–573, 1954. http://dx.doi.org/10.1098/rspa.1954.0180.
- E. Yusufoǧlu. A homotopy perturbation algorithm to solve a system of Fredholm-Volterra type integral equations. Mathematical and Computer Modelling, 47:1099–1107, 2008.