Exponentially fitted difference scheme for singularly perturbed mixed integro-differential equations

References

[1] O. Abu Arqub, An iterative method for solving fourth-order boundary value problems of mixed type integro-differential equations, J. Comput. Anal. Appl. 18 (2015), no. 5, 857–874. Suche in Google Scholar

[2] M. Al-Smadi, O. Abu Arqub and S. Momani, A computational method for two-point boundary value problems of fourth-order mixed integrodifferential equations, Math. Probl. Eng. 2013 (2013), Article ID 832074. 10.1155/2013/832074Suche in Google Scholar

[3] G. M. Amiraliyev, M. E. Durmaz and M. Kudu, Uniform convergence results for singularly perturbed Fredholm integro-differential equation, J. Math. Anal. 9 (2018), no. 6, 55–64. Suche in Google Scholar

[4] G. M. Amiraliyev, M. E. Durmaz and M. Kudu, Fitted second order numerical method for a singularly perturbed Fredholm integro-differential equation, Bull. Belg. Math. Soc. Simon Stevin 27 (2020), no. 1, 71–88. 10.36045/bbms/1590199305Suche in Google Scholar

[5] G. M. Amiraliyev and Y. D. Mamedov, Difference schemes on the uniform mesh for singular perturbed pseudo-parabolic equations, Turkish J. Math. 19 (1995), no. 3, 207–222. Suche in Google Scholar

[6] S. Amiri, M. Hajipour and D. Baleanu, A spectral collocation method with piecewise trigonometric basis functions for nonlinear Volterra–Fredholm integral equations, Appl. Math. Comput. 370 (2020), Article ID 124915. 10.1016/j.amc.2019.124915Suche in Google Scholar

[7] E. Banifatemi, M. Razzaghi and S. Yousefi, Two-dimensional Legendre wavelets method for the mixed Volterra–Fredholm integral equations, J. Vib. Control 13 (2007), no. 11, 1667–1675. 10.1177/1077546307078751Suche in Google Scholar

[8] M. S. Bani Issa, A. A. Hamoud, K. P. Ghadle and Giniswamy, Hybrid method for solving nonlinear Volterra–Fredholm integro differential equations, J. Math. Comput. Sci. 7 (2017), no. 4, 625–641. Suche in Google Scholar

[9] H. Beiglo and M. Gachpazan, Numerical solution of nonlinear mixed Volterra–Fredholm integral equations in complex plane via PQWs, Appl. Math. Comput. 369 (2020), Article ID 124828. 10.1016/j.amc.2019.124828Suche in Google Scholar

[10] N. Bellomo, B. Firmani and L. Guerri, Bifurcation analysis for a nonlinear system of integro-differential equations modelling tumor-immune cells competition, Appl. Math. Lett. 12 (1999), no. 2, 39–44. 10.1016/S0893-9659(98)00146-3Suche in Google Scholar

[11] M. I. Berenguer, D. Gámez and A. J. López Linares, Fixed point techniques and Schauder bases to approximate the solution of the first order nonlinear mixed Fredholm–Volterra integro-differential equation, J. Comput. Appl. Math. 252 (2013), 52–61. 10.1016/j.cam.2012.09.020Suche in Google Scholar

[12] J. Biazar, H. Ghazvini and M. Eslami, He’s homotopy perturbation method for systems of integro-differential equations, Chaos Solitons Fractals 39 (2009), no. 3, 1253–1258. 10.1016/j.chaos.2007.06.001Suche in Google Scholar

[13] T. A. Burton, Volterra Integral and Differential Equations, 2nd ed., Math. Sci. Eng. 202, Elsevier, Amsterdam, 2005. Suche in Google Scholar

[14] E. Cimen, A computational method for Volterra-integro differential equation, Erzincan Univ. J. Sci. Technol. 11 (2018), no. 3, 347–352. 10.18185/erzifbed.435331Suche in Google Scholar

[15] E. Cimen and M. Cakir, A uniform numerical method for solving singularly perturbed Fredholm integro-differential problem, Comput. Appl. Math. 40 (2021), no. 2, Paper No. 42. 10.1007/s40314-021-01412-xSuche in Google Scholar

[16] E. Cimen and K. Enterili, An alternative method for numerical solution of Fredholm integro differential equation (in Turkish), Erzincan Univ. J. Sci. Technol. 13 (2020), no. 1, 46–53. Suche in Google Scholar

[17] R. M. Colombo, M. Garavello, F. Marcellini and E. Rossi, An age and space structured SIR model describing the Covid-19 pandemic, J. Math. Ind. 10 (2020), Paper No. 22. 10.1186/s13362-020-00090-4Suche in Google Scholar PubMed PubMed Central

[18] P. Darania and K. Ivaz, Numerical solution of nonlinear Volterra–Fredholm integro-differential equations, Comput. Math. Appl. 56 (2008), no. 9, 2197–2209. 10.1016/j.camwa.2008.03.045Suche in Google Scholar

[19] O. Diekmann, Thresholds and travelling waves for the geographical spread of infection, J. Math. Biol. 6 (1978), no. 2, 109–130. 10.1007/BF02450783Suche in Google Scholar PubMed

[20] M. E. Durmaz and G. M. Amiraliyev, A robust numerical method for a singularly perturbed Fredholm integro-differential equation, Mediterr. J. Math. 18 (2021), no. 1, Paper No. 24. 10.1007/s00009-020-01693-2Suche in Google Scholar

[21] F. S. Fadhel, A. K. O. Mezaal and S. H. Salih, Approximate solution of the linear mixed volterrafredholm integro differential equations of second kind by using variational iteration method, Al-Mustansiriyah J. Sci. 24 (2013), no. 5, 137–146. Suche in Google Scholar

[22] A. A. Hamoud and K. P. Ghadle, The combined modified Laplace with Adomian decomposition method for solving the nonlinear Volterra–Fredholm integro differential equations, J. Korean Soc. Ind. Appl. Math. 21 (2017), no. 1, 17–28. Suche in Google Scholar

[23] A. A. Hamoud and K. P. Ghadle, Existence and uniqueness of the solution for Volterra–Fredholm integro-differential equations, Zh. Sib. Fed. Univ. Mat. Fiz. 11 (2018), no. 6, 692–701. 10.17516/1997-1397-2018-11-6-692-701Suche in Google Scholar

[24] M. Inc and Y. Cherruault, A reliable method for obtaining approximate solutions of linear and nonlinear Volterra–Freholm integro-differential equations, Kybernetes 34 (2005), no. 7–8, 1034–1048. 10.1108/03684920510605858Suche in Google Scholar

[25] B. C. Iragi and J. B. Munyakazi, New parameter-uniform discretisations of singularly perturbed Volterra integro-differential equations, Appl. Math. Inf. Sci. 12 (2018), no. 3, 517–527. 10.18576/amis/120306Suche in Google Scholar

[26] B. C. Iragi and J. B. Munyakazi, A uniformly convergent numerical method for a singularly perturbed Volterra integro-differential equation, Int. J. Comput. Math. 97 (2020), no. 4, 759–771. 10.1080/00207160.2019.1585828Suche in Google Scholar

[27] B. S. H. Kashkaria and M. I. Syam, Evolutionary computational intelligence in solving a class of nonlinear Volterra–Fredholm integro-differential equations, J. Comput. Appl. Math. 311 (2017), 314–323. 10.1016/j.cam.2016.07.027Suche in Google Scholar

[28] J.-P. Kauthen, Continuous time collocation methods for Volterra–Fredholm integral equations, Numer. Math. 56 (1989), no. 5, 409–424. 10.1007/BF01396646Suche in Google Scholar

[29] A. A. Khajehnasiri, Numerical solution of nonlinear 2D Volterra–Fredholm integro-differential equations by two-dimensional triangular function, Int. J. Appl. Comput. Math. 2 (2016), no. 4, 575–591. 10.1007/s40819-015-0079-xSuche in Google Scholar

[30] F. Köhler-Rieper, C. H. F. Röhl and E. De Micheli, A novel deterministic forecast model for the Covid-19 epidemic based on a single ordinary integro-differential equations, Eur. Phys. J. Plus 135 (2020), no. 7, 1–19. 10.1140/epjp/s13360-020-00608-0Suche in Google Scholar PubMed PubMed Central

[31] M. Kudu, I. Amirali and G. M. Amiraliyev, A finite-difference method for a singularly perturbed delay integro-differential equation, J. Comput. Appl. Math. 308 (2016), 379–390. 10.1016/j.cam.2016.06.018Suche in Google Scholar

[32] K. Maleknejad, B. Basirat and E. Hashemizadeh, A Bernstein operational matrix approach for solving a system of high order linear Volterra–Fredholm integro-differential equations, Math. Comput. Modelling 55 (2012), no. 3–4, 1363–1372. 10.1016/j.mcm.2011.10.015Suche in Google Scholar

[33] D. A. Maturi and E. A. Simbawa, The modified decomposition method for solving Volterra–Fredholm integro-differential equations using Maple, Int. J. GEOMATE 18 (2020), no. 67, 84–89. 10.21660/2020.67.5780Suche in Google Scholar

[34] N. A. Mbroh, S. C. O. Noutchie and R. Y. M. Massoukou, A second order finite difference scheme for singularly perturbed Volterra integro-differential equation, Alexandria Engrg. J. 59 (2020), no. 4, 2441–2447. 10.1016/j.aej.2020.03.007Suche in Google Scholar

[35] E. Najafi, Nyström-quasilinearization method and smoothing transformation for the numerical solution of nonlinear weakly singular Fredholm integral equations, J. Comput. Appl. Math. 368 (2020), Article ID 112538. 10.1016/j.cam.2019.112538Suche in Google Scholar

[36] S. Y. Reutskiy, The backward substitution method for multipoint problems with linear Volterra–Fredholm integro-differential equations of the neutral type, J. Comput. Appl. Math. 296 (2016), 724–738. 10.1016/j.cam.2015.10.013Suche in Google Scholar

[37] N. Rohaninasab, K. Maleknejad and R. Ezzati, Numerical solution of high-order Volterra–Fredholm integro-differential equations by using Legendre collocation method, Appl. Math. Comput. 328 (2018), 171–188. 10.1016/j.amc.2018.01.032Suche in Google Scholar

[38] M. Safavi and A. A. Khajehnasiri, Numerical solution of nonlinear mixed Volterra–Fredholm integro-differential equations by two-dimensional block-pulse functions, Cogent Math. Stat. 5 (2018), no. 1, Article ID 1521084. 10.1080/25742558.2018.1521084Suche in Google Scholar

[39] X. Tao and Y. Zhang, The coupled method for singularly perturbed Volterra integro-differential equations, Adv. Difference Equ. 2019 (2019), Paper No. 217. 10.1186/s13662-019-2139-8Suche in Google Scholar

[40] M. Turkyilmazoglu, High-order nonlinear Volterra–Fredholm–Hammerstein integro-differential equations and their effective computation, Appl. Math. Comput. 247 (2014), 410–416. 10.1016/j.amc.2014.08.074Suche in Google Scholar

[41] A.-M. Wazwaz, Linear and Nonlinear Integral Equations. Methods and Applications, Higher Education Press, Beijing, 2011. 10.1007/978-3-642-21449-3Suche in Google Scholar

[42] Ö. Yapman and G. M. Amiraliyev, A novel second-order fitted computational method for a singularly perturbed Volterra integro-differential equation, Int. J. Comput. Math. 97 (2020), no. 6, 1293–1302. 10.1080/00207160.2019.1614565Suche in Google Scholar

[43] Ö. Yapman, G. M. Amiraliyev and I. Amirali, Convergence analysis of fitted numerical method for a singularly perturbed nonlinear Volterra integro-differential equation with delay, J. Comput. Appl. Math. 355 (2019), 301–309. 10.1016/j.cam.2019.01.026Suche in Google Scholar