References
- Aghazadeh, N., & Khajehnasiri, A. A. (2013). Solving nonlinear two-dimensional volterra integro-differentional equations by block-pulse functions. Mathematical Sciences, 7, 1–6. doi:10.1186/2251-7456-7-3
- Berenguer, M. I., Gámez, D., & López Linares, A. J. (2013). Fixed point techniques and Schauder bases to approximate the solution of the first order nonlinear mixed Fredholm-Volterra integro-differential equation. Journal of Computational and Applied Mathematics, 252, 52–61. doi:10.1016/j.cam.2012.09.020
- Brunner, H. (2004). Collocation methods for Volterra integral and related functional equations. Cambridge University Press, United Kingdom.
- Diekmann, O. (1978). Thresholds and traveling for the geographical spread of infection. Journal Mathematical Biologic, 6, 109–130. doi:10.1007/BF02450783
- Ebadian, A., & Khajehnasiri, A. A. (2014). Block-pulse functions and their applications to solving systems of higher-order nonlinear Volterra integro-differential equations. Electron Journal Diff Equ, 54, 1–9.
- Harmuth, H. F. (1969). Transmission of information by orthogonal functions. Springer, Berlin.
- Hesameddini, E., & Shahbazi, M. (2017). Solving system of Volterra-Fredholm integral equations with Bernstein polynomials and hybrid Bernstein block-pulse functions. Journal of Computational and Applied Mathematics, 315, 182–194. doi:10.1016/j.cam.2016.11.004
- Khajehnasiri, A. A. (2016). Numerical solution of nonlinear 2D Volterra-Fredholm integro-differential equations by two-dimensional triangular function. International Journal Applications Computation Mathematical, 2, 575–591. doi:10.1007/s40819-015-0079-x
- Kung, F. C., & Chen, S. Y. (1978). Solution of integral equations using a set of block pulse functions. Journal of the Franklin Institute, 306, 283–291. doi:10.1016/0016-0032(78)90037-6
- Maleknejad, K., Basirat, B., & Hashemizadeh, E. (2012). A Bernstein operational matrix approach for solving a system of high order linear Volterra–Fredholm integro-differential equations. Mathematical and Computer Modelling, 55, 1363–1372. doi:10.1016/j.mcm.2011.10.015
- Maleknejad, K., & Mahdiani, K. (2011). Solving nonlinear mixed Volterra-Fredholm integral equations with the two dimensional block-pulse functions using direct method. Communications in Nonlinear Sciences Numerical Simulat, 16, 3512–3519. doi:10.1016/j.cnsns.2010.12.036
- Maleknejad, K., & Mahmoudi, Y. (2004). Numerical solution of linear Fredholm integral equation by using hybrid Taylor and block–pulse functions. Applications Mathematical and Computation, 149, 799–806.
- Maleknejad, K., Sohrabi, S., & Baranji, B. (2010). Application of 2D-BPFs to nonlinear integral equations. Communication in Nonlinear Sciences Numerical Simulat, 15, 527–535. doi:10.1016/j.cnsns.2009.04.011
- Marzban, H. R., Hoseini, S. M., & Razzaghi, M. (2009). Solution of Volterra’s population model via block-pulse functions and Lagrange-interpolating polynomials. Mathematical Meth Applications Sciences, 32, 127–134. doi:10.1002/mma.1028
- Nemati, S., Lima, P. M., & Ordokhani, Y. (2013). Numerical solution of a class of two-dimensional nonlinear Volterra integral equations using Legendre polynomials. Journal of Computational and Applied Mathematics, 242, 5369. doi:10.1016/j.cam.2012.10.021
- Pachpatte, B. G. (1986). On mixed Volterra-Fredholm type integral equations. Indian Journal Pure Applications Mathematical, 17, 448–496.
- Rohaninasa, N., Maleknejad, K., & Ezzati, R. (2018). Numerical solution of high-order Volterra-Fredholm integro-differential equations by using Legendre collocation method. Applied Mathematics and Computation, (328), 171–188. doi:10.1016/j.amc.2018.01.032
- Shahmorad, S. (2005). Numerical solution of the general form linear Fredholm–Volterra integro-differential equations by the Tau method with an error estimation. Applied Mathematics and Computation, 167, 1418–1429. doi:10.1016/j.amc.2004.08.045
- Thieme, H. R. (1977). A model for the spatial spread of an epidemic. Journal Mathematical Biologic, 4, 337–351. doi:10.1007/BF00275082
- Yuzbas, S. (2015). Numerical solutions of system of linear Fredholm-Volterra integro-differential equations by the Bessel collocation method and error estimation. Applied Mathematics and Computation, 250, 320–338. doi:10.1016/j.amc.2014.10.110
- Yuzbas, S. (2016). A collocation method based on Bernstein polynomials to solve nonlinear Fredholm Volterra integro-differential equations. Applied Mathematics and Computation, 273, 142–154. doi:10.1016/j.amc.2015.09.091