- D. Adnan Maturi, “The Adomian Decomposition Method for Solving Heat Transfer Lighthill Singular Integral Equation Using Maple”, Int. J. GEOMATE 22 (89), 16-23 (2022). https://geomatejournal.com/geomate/article/view/3140 Cited May 10, 2022.
- I. V. Alexandrova, A. A. Ivanov, and D. V. Alexandrov, “Analytical Solution of Integro-Differential Equations Describing the Process of Intense Boiling of a Superheated Liquid”, Math. Methods. Appl. Sci. 13 (2021). DOI: 10.1002/mma.7560
- P. Agarwal, U. Baltaeva, and Y. Alikulov, “Solvability of the Boundary-Value Problem for a Linear Loaded Integro-Differential Equation in an Infinite Three-Dimensional Domain”, Chaos Solit. Fractals.
- A. A. Minakov and C. Schick, “Integro-Differential Equation for the Non-Equilibrium Thermal Response of Glass-Forming Materials: Analytical Solutions”, Symmetry. 13 (2021). DOI: 10.3390/sym13020256
- L. Zhang, L. Xu, and T. Yin, “An Accurate Hyper-Singular Boundary Integral Equation Method for Dynamic Poroelasticity in Two Dimensions”, (2020). https://arxiv.org/pdf/2008.07115.pdf Cited May 10, 2022.
- B. Gürbüz, “A Numerical Scheme for the Solution of NeutralIntegro-Differential Equations Including Variable Delay”, Math. Sci. 16, 13-21 (2022). DOI: 10.1007/s40096-021-00388-3
- H. Mesgarani and P. Parmour, “Application of Numerical Solution of Linear Fredholm Integral Equation of the First Kind for Image Restoration”, Math. Sci. (2022). DOI: 10.1007/s40096-022-00456-2
- M. Ghiat and H. Guebbai, “Analytical and Numerical Study for an Integro-Differential Nonlinear Volterra Equation with Weakly Singular Kernel”, Comput. Appl. Math. 37 (4), 4661-4974 (2018). DOI: 10.1007/s40314-018-0597-3
- M. Ghiat, H. Guebbai, M. Kurulay, and S. Segni, “On the Weakly Singular Integro-Differential Nonlinear Volterra Equation Depending in Acceleration Term”, Comput. Appl. Math. 39 (2020). DOI: 10.1007/s40314-020-01235-2
-
S. Segni, M. Ghiat, and H. Guebbai, "New Approximation Method for Volterra Nonlinear Integro-Differential Equation", Asian-Eur. J. Math. 12 (2019). DOI: 10.1142/S1793557119500165
-
S. Touati, M.-Z. Aissaoui, S. Lemita, and H. Guebbai, "Investigation Approach for a Nonlinear Singular Fredholm Integro-Differential Equation", Bol. Soc. Paran. Mat. 40 (2022). DOI: 10.5269/bspm.46898
-
H. Guebbai and L. Grammont, "A New Degenerate Kernel Method for a Weakly Singular Integral Equation", Appl. Math. Comput. 230, 414-427 (2014). DOI: 10.1016/j.amc.2013.12.102
-
S. Touati, S. Lemita, M. Ghiat, and M.-Z. Aissaoui, "Solving a Nonlinear Volterra-Fredholm Integro-Differential Equation with Weakly Singular Kernels", Fasc. Math. 62 (1), 155-168 (2019). http://fasciculi-mathematici.put.poznan.pl/ Cited May 10, 2022.
-
A. Jafarian, R. Rezaei, and A. K. Golmankhaneh, "On Solving Fractional Higher-Order Equations via Artificial Neural Networks", Iran. J. Sci. Technol. Trans. A: Sci. (2022). DOI: 10.1007/s40995-021-01254-6
-
M. Bohner, O. Tunç, and C. Tunç, "Qualitative Analysis of Caputo Fractional Integro-Differential Equations with Constant Delays", Comp. Appl. Math. 40 (2021). DOI: 10.1007/s40314-021-01595-3
-
S. Noeiaghdam, S. Micula, and J. J. Nieto, "A Novel Technique to Control the Accuracy of a Nonlinear Fractional Order Model of COVID-19: Application of the CESTAC Method and the CADNA Library", Mathematics 9 (2021). DOI: 10.3390/math9121321
-
K. Atkinson and W. Han, Theoretical Numerical Analysis: A Functional Analysis Framework (Springer, New York, 2001).
-
P. Assari, "Solving Weakly Singular Integral Equations Utilizing the Meshless Local Discrete Collocation Technique", Alex. Eng. J. 57 (4), 2497-2507 (2018). DOI: 10.1016/j.aej.2017.09.015 EDN: XAPBKD
-
A. Mennouni, "A Projection Method for Solving Cauchy Singular Integro-Differential Equations", Appl. Math. Lett. 25 (6), 986-989 (2012). 10.1016/j.aml.2011.11.012 Cited May 10, 2022. DOI: 10.1016/j.aml.2011.11.012CitedMay10 EDN: PKYBAJ
-
H. Guebbai, "Regularization and Fourier Series for Fredholm Integral Equations of the Second Kind with a Weakly Singular Kernel", Numer. Funct. Anal. Optim. 39 (2018). DOI: 10.1080/01630563.2017.1364753
-
B. Tair, H. Guebbai, S. Segni, and M. Ghiat, "Solving Linear Fredholm Integro-Differential Equation by Nystöm Method", J. Appl. Math. Comput. Mech. 20 (3), 53-64 (2021). DOI: 10.17512/jamcm.2021.3.05
-
B. Tair, H. Guebbai, S. Segni, and M. Ghiat, "An Approximation Solution of Linear Fredholm Integro-Differential Equation Using Collocation and Kantorovich Methods", J. Appl. Math. Comput. (2021). DOI: 10.1007/s12190-021-01654-2 EDN: EPAYVP
-
M. K. Kadalbajoo and P. Arora, "B-Spline Collocation Method for the Singular-Perturbation Problem Using Artificial Viscosity", Comput. Math. Appl. 57 (4), 650-663 (2009). DOI: 10.1016/j.camwa.2008.09.008
-
R. Firouzdor, A. Heidarnejad Khoob, and Z. Mollaramezani, "Numerical Solution of Functional Integral Equations by Using B-Splines", J. Linear Topol. Algebra 1 (1), 45-53 (2012). https://oaji.net/articles/2014/1011-1405094276.pdf Cited May 10, 2022.
-
M. Gholamian, J. Saberi-Nadjafi, and A. R. Soheili, "Cubic B-Splines Collocation Method for Solving a Partial Integro-Differential Equation with a Weakly Singular Kernel", Comput. Methods Differ. Equ. 7 (3), 497-510 (2019). https://www.sid.ir/en/journal/ViewPaper.aspx?id=695385 Cited May 10, 2022.
-
J. Rashidinia, E. Babolian, and Z. Mahmood, "Spline Collocation for Fredholm Integral Equations", Math. Sci. 5 (2), 147-158 (2011). https://www.sid.ir/en/journal/ViewPaper.aspx?id=250639 Cited May 10, 2022.
-
R. A. Adams and J. J. F. Fournier, Sobolev Spaces (Academic Press, Amsterdam, 2003).
-
A. Bashan, N. M. Yagmurlu, Y. Ucar, and A. Esen, "An Effective Approach to Numerical Solutions for the Schrödinger Equation Via Modified Cubic B-Spline Differential Quadrature Method", Chaos Solit. Fractals 100, 45-56 (2017). DOI: 10.1016/j.chaos.2017.04.038
-
N. Ebrahimi and J. Rashidinia, "Spline Collocation for Fredholm and Volterra Integro-Differential Equations", Int. J. Math. Model. Comput. 4 (3), 289-298 (2014). https://www.sid.ir/en/journal/ViewPaper.aspx?id=412805 Cited May 10, 2022.
-
Kh. Maleknejad and Y. Rostami, "B-Spline Method for Solving Fredholm Integral Equations of the First Kind", Int. J. Ind. Math. 11 (1), 63-70 (2019). https://www.sid.ir/en/journal/ViewPaper.aspx?id=715404 Cited May 10, 2022.
-
G. Birkhoff and C. de Boor, "Error Bounds for Spline Interpolation", J. Math. Mech. 13 (5), 827-835 (1964). http://www.jstor.org/stable/24901235 Cited May 10, 2022.
-
J. H. Ahlberg, E. N. Nilson, and J. L. Walsh, The Theory of Splines and Their Applications (Academic Press, New York, 1967).
-
E. V. Shikin and I. P. Alexander, Handbook on Splines for the User (CRC Press, Boca Raton, 1995).
-
W. J. Kammerer and G. W. Reddien, "Local Convergence of Smooth Cubic Spline Interpolates", SIAM J. Numer. Anal. 9 (4), 687-694 (1972). DOI: 10.1137/0709057
-
P. M. Prenter, Splines and Variational Methods (Wiley, New York, 1989).
-
T. R. Lucas, "Error Bounds for Interpolating Cubic Splines under Various End Conditions", SIAM J. Numer. Anal. 11 (3), 569-584 (1974). DOI: 10.1137/0711049
-
Yu. S. Volkov, "Convergence Analysis of an Interpolation Process for the Derivatives of a Complete Spline", J. Math. Sci. 187 (1), 101-114 (2012). DOI: 10.1007/s10958-012-1053-3 EDN: YQHAIH
-
G. D. Andria, G. D. Byrne, and C. A. Hall, "Convergence of Cubic Spline Interpolants of Functions Possessing Discontinuities", J. Approx. Theory 8 (2), 150-159 (1973). DOI: 10.1016/0021-9045(73)90024-5
-
K. E. Atkinson, "On the Order of Convergence of Natural Cubic Spline Interpolation", SIAM J. Numer. Anal, 5 (1), 89-101 (1968). DOI: 10.1137/0705007
-
Yu. S. Volkov, "Obtaining a Banded System of Equations in Complete Spline Interpolation Problem Via B-Spline Basis", Cent. Eur. J. Math. 10 (1), 352-356 (2012). DOI: 10.2478/s11533-011-0104-1 EDN: PDGKRX
-
L. L. Schumaker, Spline Functions: Basic Theory (Wiley, New York, 1981).
-
M. Ahues, A. Largillier, and B. V. Limaye, Spectral Computations for Bounded Operators (CRC Press, Boca Raton, 2001).
-
S. M. Zemyan, The Classical Theory of Integral Equations (Birkhäuser/Springer, New York, 2012).
