یک روش عددی مبتنی بر توابع متعامد لگاریتمی تعمیم یافته برای حل معادلات انتگرال ولترای کوردیال نوع سوم

[1] Allaei, S.S., Yang, Z.W. and Brunner, H., 2015. Journal of Integral Equations and Applications, 27, pp.325−342. doi: 10.1216/JIE­2015­27­3­325
[2] Bart, G.R. and Warnock, R.L., 1973. Linear integral equations of the third kind. SIAM Journal on
Mathematical Analysis, 4(4), pp.609−622. doi: 10.1137/0504053

[3] Bareiss, E.H. and Abu­Shumays, I.K., 1969. On the structure of isotropic transport operators in space. Transport Theory, SIAM­AMS Proceedings, AMS, Providence, Rhode Island, 1 pp.37−78.
[4] Bhat, I.A. and Mishra, L.N., 2022. Numerical solutions of Volterra integral equations of third kind and its convergence analysis. Symmetry, 14(12), pp.2600. doi: 10.3390/sym14122600
[5] Boyd, J.P., 2001. Chebyshev and Fourier spectral methods. Courier Dover Publications.
[6] Boyd, J.P., 1987. Exponentially convergent Fourier­Chebshev quadrature schemes on bounded and infinite intervals. Journal of scientific computing, 2, pp.99−109. doi: 10.1007/BF01061480
[7] Boyd, J.P., 1987. Spectral methods using rational basis functions on an infinite interval. Journal of computational physics, 69(1), pp.112−142. doi: 0021999187901586
[8] Brunner, H., 2017. Volterra Integral Equations: An Introduction to Theory and Applications (Vol. 30). Cambridge University Press.
[9] Case, K.M., and Zweifel, P.F., 1967. Linear Transport Theory. Addison−Wesley Publishing Company Reading Massachusetts.
[10] Chen, S. and Shen, J., 2018. Enriched spectral methods and applications to problems with weakly singular solutions. Journal of Scientific Computing, 77(3), pp.1468−1489. doi: 10.1007/s10915­018­0862­z
[11] Chen, S. and Shen, J., 2020. An efficient and accurate numerical method for the spectral fractional Laplacian equation. Journal of Scientific Computing, 82(1), pp.17. doi: 10.1007/s10915­019­01122­x
[12] Chen, S. and Shen, J., 2022. Log orthogonal functions: approximation properties and applications. IMA Journal of Numerical Analysis, 42(1), pp.712−743. doi: 10.1093/imanum/draa087
[13] Darbenas, Z. and Oliver, M., 2019. Uniqueness of solutions for weakly degenerate cordial Volterra integral equations. Journal of Integral Equations and Applications, 31, pp.307−327. doi: 10.1216/JIE2019­31­3­307
[14] Diogo, T. and Vainikko, G., 2013. Applicability of spline collocation to cordial Volterra equations. Mathematical Modelling and Analysis, 18(1), pp.1−21. doi: 10.3846/13926292.2013.756072
[15] Firoozjaee, M.A., 2021, November. Numerical solution of a class of third­kind Volterra integral equations using Ritz approximation. In Proceedings of the 6th International Conference on Combinatorics, Cryptography, Computer Science and Computing, Tehran, Iran, pp. 17−18.
[16] Kangro, U., 2017. Cordial Volterra integral equations and singular fractional integro­differential equations in spaces of analytic functions. Mathematical Modelling and Analysis, 22(4), pp.548−567. doi: 10.3846/13926292.2017.1333970
[17] Majidian, H., 2017. Efficient quadrature rules for a class of cordial Volterra integral equations: A comparative study. Bulletin of the Iranian Mathematical Society, 43(5), pp.1245−1258.
[18] Morin, P., Nochetto, R.H. and Siebert, K.G., 2002. Convergence of adaptive finite element methods. SIAM review, 44(4), pp.631−658. doi: 10.1137/S0036144502409093
[19] Nemati, S. and Lima, P.M., 2018. Numerical solution of a third­kind Volterra integral equation using an operational matrix technique. In 2018 European Control Conference (ECC), (pp. 3215−3220). IEEE. doi: 10.23919/ECC.2018.8550223

[20] Nemati, S., Lima, P.M. and Torres, D.F., 2021. Numerical solution of a class of third­kind
Volterra integral equations using Jacobi wavelets. Numerical Algorithms, 86, pp.675−691. doi:
10.48550/arXiv.2002.04736
[21] Schumack, M.R., Schultz, W.W. and Boyd, J.P., 1991. Spectral method solution of the Stokes equations on nonstaggered grids. Journal of Computational Physics, 94(1), pp.30−58. doi: 10.1016/0021­9991(91)90136­9
[22] Shayanfard, F., Dastjerdi, H.L. and Ghaini, F.M., 2019. A numerical method for solving Volterra integral equations of the third kind by multistep collocation method. Computational and Applied Mathematics, 38, pp.1−13. doi: 10.1007/s40314­019­0947­9
[23] Shen, J. and Wang, L.L., 2004. Error analysis for mapped Legendre spectral and pseudospectral methods. SIAM journal on numerical analysis, 42(1), pp.326−349. doi: 10.1137/S0036142903422065
[24] Shen, J. and Wang, Y., 2016. Müntz–Galerkin Methods and Applications to Mixed
Dirichlet–Neumann Boundary Value Problems. SIAM Journal on Scientific Computing, 38(4),
pp.A2357−A2381. doi:10.1137/15M1052391
[25] Shen, J., Tang, T. and Wang, L.L., 2011. Spectral methods: algorithms, analysis and applications (Vol. 41). Springer Science & Business Media.
[26] Strang, G. and Fix, G.J., 1973. An Analysis of the Finite Element Method. Prentice­Hall Series in
Automatic Computation, Englewood Cliffs, N. J: Prentice­Hall, Inc.
[27] Usta, F., 2021. Bernstein approximation technique for numerical solution of Volterra integral equations of the third kind. Computational and Applied Mathematics, 40(5), pp.161. doi: 10.1007/s40314­021­01555­x
[28] Vainikko, G., 2009. Cordial Volterra integral equations 1. Numerical Functional Analysis and Optimization, 30(9­10), pp.1145−1172. doi: 10.1080/01630560903393188
[29] Vainikko, G., 2010. Cordial Volterra integral equations 2. Numerical functional analysis and optimization, 31(2), pp.191−219. doi: 10.1080/01630561003666234
[30] Vainikko, G., 2010. Spline collocation for cordial Volterra integral equations. Numerical functional analysis and optimization, 31(3), pp.313−338. doi: 10.1080/01630561003757710
[31] Vainikko, G., 2010. Spline collocation­interpolation method for linear and nonlinear cordial
Volterra integral equations. Numerical functional analysis and optimization, 32(1), pp.83−109. doi:
10.1080/01630563.2010.526412
[32] Wang, L.L. and Shen, J., 2005. Error analysis for mapped Jacobi spectral methods. Journal of Scientific Computing, 24, pp.183−218. doi: 10.1007/s10915­004­4613­y
[33] Yang, Z.W., 2015. Second­kind linear Volterra integral equations with noncompact operators. Numerical Functional Analysis and Optimization, 36(1), pp.104−131. doi: 10.1080/01630563.2014.9517