Liao, Shijun Avoiding small denominator problems by means of the homotopy analysis method. (English) Zbl 1524.65301 Adv. Appl. Math. Mech. 15, No. 2, 267-299 (2023). MSC: 65L99 34A25 34C25 41A58 PDFBibTeX XMLCite \textit{S. Liao}, Adv. Appl. Math. Mech. 15, No. 2, 267--299 (2023; Zbl 1524.65301) Full Text: DOI arXiv
Gerner, Wadim Properties of the Biot-Savart operator acting on surface currents. arXiv:2311.03108 Preprint, arXiv:2311.03108 [math-ph] (2023). MSC: 14J81 41A35 55P99 78A30 78A46 78A55 BibTeX Cite \textit{W. Gerner}, ``Properties of the Biot-Savart operator acting on surface currents'', Preprint, arXiv:2311.03108 [math-ph] (2023) Full Text: arXiv OA License
Kumbinarasaiah, S.; Preetham, M. P. A study on homotopy analysis method and Clique polynomial method. (English) Zbl 07665255 Comput. Methods Differ. Equ. 10, No. 3, 774-788 (2022). MSC: 65L05 34A12 41A10 34A45 PDFBibTeX XMLCite \textit{S. Kumbinarasaiah} and \textit{M. P. Preetham}, Comput. Methods Differ. Equ. 10, No. 3, 774--788 (2022; Zbl 07665255) Full Text: DOI
Al-Qudah, Alaa; Odibat, Zaid; Shawagfeh, Nabil An optimal homotopy analysis transform method for handling nonlinear PDEs. (English) Zbl 1505.65282 Int. J. Appl. Comput. Math. 8, No. 5, Paper No. 260, 19 p. (2022). MSC: 65M99 44A10 41A58 65M12 34A34 35Q53 PDFBibTeX XMLCite \textit{A. Al-Qudah} et al., Int. J. Appl. Comput. Math. 8, No. 5, Paper No. 260, 19 p. (2022; Zbl 1505.65282) Full Text: DOI
Fernández, Francisco M. Comment on: “Removing non-smoothness in solving Black-Scholes equation using a perturbation method”. (English) Zbl 1514.83023 Phys. Lett., A 452, Article ID 128446, 2 p. (2022). MSC: 83C57 35B65 35B20 41A58 PDFBibTeX XMLCite \textit{F. M. Fernández}, Phys. Lett., A 452, Article ID 128446, 2 p. (2022; Zbl 1514.83023) Full Text: DOI
Argyros, Ioannis K.; Sharma, Debasis; Parhi, Sanjaya Kumar; Sunanda, Shanta Kumari A study on the local convergence and complex dynamics of Kou’s family of iterative methods. (English) Zbl 1501.39008 S\(\vec{\text{e}}\)MA J. 79, No. 2, 365-381 (2022). MSC: 39B12 37F10 41A25 47J25 65J15 65Y20 65H20 PDFBibTeX XMLCite \textit{I. K. Argyros} et al., S\(\vec{\text{e}}\)MA J. 79, No. 2, 365--381 (2022; Zbl 1501.39008) Full Text: DOI
Ljajko, Eugen; Tošić, Marina; Kevkić, Tijana; Stojanović, Vladica Application of the HPM in approximation PDFs of non-linear time series. (English) Zbl 1513.62033 Sci. Bull., Ser. A, Appl. Math. Phys., Politeh. Univ. Buchar. 83, No. 2, 177-186 (2021). MSC: 62E17 60E10 41A46 42B10 62M10 PDFBibTeX XMLCite \textit{E. Ljajko} et al., Sci. Bull., Ser. A, Appl. Math. Phys., Politeh. Univ. Buchar. 83, No. 2, 177--186 (2021; Zbl 1513.62033)
Arafa, Anas A. M.; Hagag, Ahmed M. Sh. A different approach for study some fractional evolution equations. (English) Zbl 1476.35293 Anal. Math. Phys. 11, No. 4, Paper No. 162, 21 p. (2021). MSC: 35R11 35A22 41A58 PDFBibTeX XMLCite \textit{A. A. M. Arafa} and \textit{A. M. Sh. Hagag}, Anal. Math. Phys. 11, No. 4, Paper No. 162, 21 p. (2021; Zbl 1476.35293) Full Text: DOI
Telen, Simon; Van Barel, Marc; Verschelde, Jan A robust numerical path tracking algorithm for polynomial homotopy continuation. (English) Zbl 1457.65023 SIAM J. Sci. Comput. 42, No. 6, A3610-A3637 (2020). MSC: 65H20 65H04 65H10 41A21 PDFBibTeX XMLCite \textit{S. Telen} et al., SIAM J. Sci. Comput. 42, No. 6, A3610--A3637 (2020; Zbl 1457.65023) Full Text: DOI arXiv
Veeresha, Pundikala; Prakasha, Doddabhadrappla Gowda; Baleanu, Dumitru Analysis of fractional Swift-Hohenberg equation using a novel computational technique. (English) Zbl 1446.35256 Math. Methods Appl. Sci. 43, No. 4, 1970-1987 (2020). MSC: 35R11 26A33 41A58 PDFBibTeX XMLCite \textit{P. Veeresha} et al., Math. Methods Appl. Sci. 43, No. 4, 1970--1987 (2020; Zbl 1446.35256) Full Text: DOI
Shklyaev, Konstantin S. A connected compact locally Chebyshev set in a finite-dimensional space is a Chebyshev set. (English. Russian original) Zbl 1471.41015 Sb. Math. 211, No. 3, 455-465 (2020); translation from Mat. Sb. 211, No. 3, 158-168 (2020). Reviewer: Sergei S. Platonov (Petrozavodsk) MSC: 41A65 PDFBibTeX XMLCite \textit{K. S. Shklyaev}, Sb. Math. 211, No. 3, 455--465 (2020; Zbl 1471.41015); translation from Mat. Sb. 211, No. 3, 158--168 (2020) Full Text: DOI
Liu, Tianbao; Qin, Xiwen; Li, Qiuyue An optimal fourth-order family of modified Cauchy methods for finding solutions of nonlinear equations and their dynamical behavior. (English) Zbl 1442.65089 Open Math. 17, 1567-1598 (2019). Reviewer: Anton Iliev (Plovdiv) MSC: 65H05 37N30 65H20 41A21 PDFBibTeX XMLCite \textit{T. Liu} et al., Open Math. 17, 1567--1598 (2019; Zbl 1442.65089) Full Text: DOI
Weinberger, Shmuel Interpolation, the rudimentary geometry of spaces of Lipschitz functions, and geometric complexity. (English) Zbl 1447.57036 Found. Comput. Math. 19, No. 5, 991-1011 (2019). MSC: 57R75 41A10 55Q05 68T05 PDFBibTeX XMLCite \textit{S. Weinberger}, Found. Comput. Math. 19, No. 5, 991--1011 (2019; Zbl 1447.57036) Full Text: DOI
Stojanović, Vladica; Kevkić, Tijana; Jelić, Gordana; Randjelović, Dragan Determination of invariant measures: an approach based on homotopy perturbations. (English) Zbl 1424.62014 Sci. Bull., Ser. A, Appl. Math. Phys., Politeh. Univ. Buchar. 80, No. 2, 119-128 (2018). MSC: 62E17 60E10 41A46 42B10 PDFBibTeX XMLCite \textit{V. Stojanović} et al., Sci. Bull., Ser. A, Appl. Math. Phys., Politeh. Univ. Buchar. 80, No. 2, 119--128 (2018; Zbl 1424.62014)
Al-Saar, Fawziah M.; Ghadle, Kirtiwant P. Combined Laplace transform with analytical methods for solving Volterra integral equations with a convolution kernel. (English) Zbl 1411.44001 J. Korean Soc. Ind. Appl. Math. 22, No. 2, 125-136 (2018). MSC: 44A10 41A58 65H20 65R20 PDFBibTeX XMLCite \textit{F. M. Al-Saar} and \textit{K. P. Ghadle}, J. Korean Soc. Ind. Appl. Math. 22, No. 2, 125--136 (2018; Zbl 1411.44001)
Vahidi, A. R.; Babolian, E.; Azimzadeh, Z. An improvement to the homotopy perturbation method for solving nonlinear Duffing’s equations. (English) Zbl 1448.65066 Bull. Malays. Math. Sci. Soc. (2) 41, No. 2, 1105-1117 (2018). Reviewer: Bülent Karasözen (Ankara) MSC: 65L05 65L12 34A45 41A21 PDFBibTeX XMLCite \textit{A. R. Vahidi} et al., Bull. Malays. Math. Sci. Soc. (2) 41, No. 2, 1105--1117 (2018; Zbl 1448.65066) Full Text: DOI
Stojanović, Vladica; Kevkić, Tijana; Jelić, Gordana Application of the homotopy analysis method in approximation of convolutions stochastic distributions. (English) Zbl 1513.62034 Sci. Bull., Ser. A, Appl. Math. Phys., Politeh. Univ. Buchar. 79, No. 4, 103-112 (2017). MSC: 62E17 60E10 41A46 42B10 PDFBibTeX XMLCite \textit{V. Stojanović} et al., Sci. Bull., Ser. A, Appl. Math. Phys., Politeh. Univ. Buchar. 79, No. 4, 103--112 (2017; Zbl 1513.62034)
Akram, Ghazala; Nadeem, Zara Nonpolynomial spline technique for the solution of ninth order boundary value problems. (English) Zbl 1424.65103 Turk. J. Math. 41, No. 2, 312-325 (2017). MSC: 65L10 34A45 41A15 65D07 PDFBibTeX XMLCite \textit{G. Akram} and \textit{Z. Nadeem}, Turk. J. Math. 41, No. 2, 312--325 (2017; Zbl 1424.65103) Full Text: DOI
Kozak, Jernej; Krajnc, Marjeta; Vitrih, Vito \(G^1\) interpolation by rational cubic PH curves in \(\mathbb R^3\). (English) Zbl 1417.65061 Comput. Aided Geom. Des. 42, 7-22 (2016). MSC: 65D05 41A05 41A20 PDFBibTeX XMLCite \textit{J. Kozak} et al., Comput. Aided Geom. Des. 42, 7--22 (2016; Zbl 1417.65061) Full Text: DOI
Turkyilmazoglu, M. Is homotopy perturbation method the traditional Taylor series expansion. (English) Zbl 1396.41024 Hacet. J. Math. Stat. 44, No. 3, 651-657 (2015). MSC: 41A58 PDFBibTeX XMLCite \textit{M. Turkyilmazoglu}, Hacet. J. Math. Stat. 44, No. 3, 651--657 (2015; Zbl 1396.41024)
Odibat, Zaid; Bataineh, A. Sami An adaptation of homotopy analysis method for reliable treatment of strongly nonlinear problems: construction of homotopy polynomials. (English) Zbl 1318.34021 Math. Methods Appl. Sci. 38, No. 5, 991-1000 (2015). MSC: 34A45 34A12 34A34 41A58 PDFBibTeX XMLCite \textit{Z. Odibat} and \textit{A. S. Bataineh}, Math. Methods Appl. Sci. 38, No. 5, 991--1000 (2015; Zbl 1318.34021) Full Text: DOI
Jaharuddin Homotopy perturbation method for a SEIR model with varying total population size. (English) Zbl 1303.34039 Far East J. Math. Sci. (FJMS) 84, No. 2, 187-198 (2014). MSC: 34C60 34A25 34A34 41A10 34A45 92D30 PDFBibTeX XMLCite \textit{Jaharuddin}, Far East J. Math. Sci. (FJMS) 84, No. 2, 187--198 (2014; Zbl 1303.34039) Full Text: Link
Yildirim, Ahmet; Koçak, Hüseyin An efficient technique for solving the Blaszak-Marciniak lattice by combining homotopy perturbation and Padé techniques. (English) Zbl 1359.65103 Int. J. Comput. Methods 9, No. 2, Article ID 1240024, 16 p. (2012). MSC: 65L03 34A33 34A45 41A21 PDFBibTeX XMLCite \textit{A. Yildirim} and \textit{H. Koçak}, Int. J. Comput. Methods 9, No. 2, Article ID 1240024, 16 p. (2012; Zbl 1359.65103) Full Text: DOI
Zurigat, Mohammad; Momani, Shaher; Alawneh, Ahmad Solving nonlinear oscillators using a modified homotopy analysis method. (English) Zbl 1289.65158 Stud. Univ. Babeș-Bolyai, Math. 57, No. 4, 579-588 (2012). MSC: 65L05 34A34 34C10 44A10 41A21 34A25 PDFBibTeX XMLCite \textit{M. Zurigat} et al., Stud. Univ. Babeș-Bolyai, Math. 57, No. 4, 579--588 (2012; Zbl 1289.65158)
Jafari, H.; Tajadodi, H.; Matikolai, S. A. Hosseini Homotopy perturbation pade technique for solving fractional Riccati differential equations. (English) Zbl 1401.34011 Int. J. Nonlinear Sci. Numer. Simul. 11, No. Supplement, 271-276 (2010). MSC: 34A08 34A25 41A21 PDFBibTeX XMLCite \textit{H. Jafari} et al., Int. J. Nonlinear Sci. Numer. Simul. 11, No. Supplement, 271--276 (2010; Zbl 1401.34011) Full Text: DOI
Liao, Shijun On the relationship between the homotopy analysis method and Euler transform. (English) Zbl 1221.65206 Commun. Nonlinear Sci. Numer. Simul. 15, No. 6, 1421-1431 (2010). MSC: 65L99 34E10 34A45 41A58 40G05 PDFBibTeX XMLCite \textit{S. Liao}, Commun. Nonlinear Sci. Numer. Simul. 15, No. 6, 1421--1431 (2010; Zbl 1221.65206) Full Text: DOI
Rangarajan, R.; Muneer Basha, H. Numerical-analytic methods for nonlinear diffusion type differential equations of heat transfer. (English) Zbl 1225.65099 J. Indian Math. Soc., New Ser. 77, No. 1-4, 159-166 (2010). MSC: 65M70 35K55 34B16 41A21 65L10 PDFBibTeX XMLCite \textit{R. Rangarajan} and \textit{H. Muneer Basha}, J. Indian Math. Soc., New Ser. 77, No. 1--4, 159--166 (2010; Zbl 1225.65099)
Odibat, Zaid M. A study on the convergence of homotopy analysis method. (English) Zbl 1203.65105 Appl. Math. Comput. 217, No. 2, 782-789 (2010). Reviewer: Werner M. Seiler (Kassel) MSC: 65L05 41A58 34A25 34A34 65L70 PDFBibTeX XMLCite \textit{Z. M. Odibat}, Appl. Math. Comput. 217, No. 2, 782--789 (2010; Zbl 1203.65105) Full Text: DOI
Chen, Ruyun; Liang, Ximing Asymptotic expansions of Bessel, Anger and Weber transformations. (English) Zbl 1200.65018 J. Math. Anal. Appl. 372, No. 2, 377-389 (2010). Reviewer: Manfred Tasche (Rostock) MSC: 65D32 41A55 65R10 44A20 33C10 PDFBibTeX XMLCite \textit{R. Chen} and \textit{X. Liang}, J. Math. Anal. Appl. 372, No. 2, 377--389 (2010; Zbl 1200.65018) Full Text: DOI
Yıldırım, Ahmet; Sezer, Sefa Anıl Non-perturbative solution of three-dimensional Navier-Stokes equations for the flow near an infinite rotating disk. (English) Zbl 1197.35198 Math. Methods Appl. Sci. 33, No. 11, 1298-1305 (2010). MSC: 35Q30 35A20 76D05 76M45 41A21 PDFBibTeX XMLCite \textit{A. Yıldırım} and \textit{S. A. Sezer}, Math. Methods Appl. Sci. 33, No. 11, 1298--1305 (2010; Zbl 1197.35198) Full Text: DOI
Odibat, Zaid M. On the approximation of integrals using homotopy perturbation method. (English) Zbl 1182.65047 Int. J. Comput. Math. 87, No. 1, 53-62 (2010). MSC: 65D32 41A55 PDFBibTeX XMLCite \textit{Z. M. Odibat}, Int. J. Comput. Math. 87, No. 1, 53--62 (2010; Zbl 1182.65047) Full Text: DOI
Chen, Ruyun; Xiang, Shuhuang Note on the homotopy perturbation method for multivariate vector-value oscillatory integrals. (English) Zbl 1177.65042 Appl. Math. Comput. 215, No. 1, 78-84 (2009). Reviewer: Manfred Tasche (Rostock) MSC: 65D32 42B10 41A55 41A63 65T40 PDFBibTeX XMLCite \textit{R. Chen} and \textit{S. Xiang}, Appl. Math. Comput. 215, No. 1, 78--84 (2009; Zbl 1177.65042) Full Text: DOI
Merdan, Mehmet Homotopy perturbation method for solving human T-cell lymphotropic virus I (HTLV-I) infection of Cd4\(^+\) T-cells model. (English) Zbl 1166.92028 Math. Comput. Appl. 14, No. 2, 85-96 (2009). MSC: 92C50 41A21 65L99 34A34 PDFBibTeX XMLCite \textit{M. Merdan}, Math. Comput. Appl. 14, No. 2, 85--96 (2009; Zbl 1166.92028) Full Text: DOI
Micula, Sanda; Wendland, Wolfgang L. Spline approximation of a non-linear Riemann-Hilbert problem. (English) Zbl 1163.41001 Appl. Anal. 87, No. 9, 1067-1083 (2008). Reviewer: Vasily A. Chernecky (Odessa) MSC: 41A15 35J65 47H10 47H11 65R20 30E25 34B16 PDFBibTeX XMLCite \textit{S. Micula} and \textit{W. L. Wendland}, Appl. Anal. 87, No. 9, 1067--1083 (2008; Zbl 1163.41001) Full Text: DOI
Molabahrami, A.; Khani, F. Numerical solutions of highly oscillatory integrals. (English) Zbl 1139.65019 Appl. Math. Comput. 198, No. 2, 657-664 (2008). MSC: 65D32 41A55 PDFBibTeX XMLCite \textit{A. Molabahrami} and \textit{F. Khani}, Appl. Math. Comput. 198, No. 2, 657--664 (2008; Zbl 1139.65019) Full Text: DOI
Siyyam, Hani I.; Jaradat, Emad Ali Line integrals over implicitly defined curves. (English) Zbl 1146.65026 Pac.-Asian J. Math. 1, No. 1, 61-80 (2007). MSC: 65D32 41A55 34A34 65L06 65L05 65H20 65L50 PDFBibTeX XMLCite \textit{H. I. Siyyam} and \textit{E. A. Jaradat}, Pac.-Asian J. Math. 1, No. 1, 61--80 (2007; Zbl 1146.65026)
Hang, Fengbo; Lin, Fanghua Topology of Sobolev mappings. IV. (English) Zbl 1093.46017 Discrete Contin. Dyn. Syst. 13, No. 5, 1097-1124 (2005). Reviewer: Neculai Papaghiuc (Iaşi) MSC: 46E35 58D15 41A29 PDFBibTeX XMLCite \textit{F. Hang} and \textit{F. Lin}, Discrete Contin. Dyn. Syst. 13, No. 5, 1097--1124 (2005; Zbl 1093.46017) Full Text: DOI
Andersen, J. E.; Askitas, N.; Bar-Natan, D.; Baseilhac, S.; Benedetti, R.; Bigelow, S.; Boileau, M.; Bott, R.; Carter, J. S.; Deloup, F.; Dunfield, N.; Fenn, R.; Ferrand, E.; Garoufalidis, S.; Goussarov, M.; Guadagnini, E.; Habiro, H.; Hansen, S. K.; Harikae, T.; Haviv, A.; Jeong, M. -J.; Jones, V.; Kashaev, R.; Kawahigashi, Y.; Kerler, T.; Kidwell, M.; Kohno, T.; Kricker, A.; Le, T. T. Q.; Lescop, C.; Lin, X. -S.; Masbaum, G.; Massuyeau, G.; Morita, S.; Morton, H. R.; Murakami, H.; Murakami, J.; Nakanishi, Y.; Ohtsuki, T.; Ohyama, Y.; Okamoto, M.; Okuda, N.; Park, C. -Y.; Pilo, L.; Polyak, M.; Przytycki, J.; Roberts, J.; Rourke, C.; Rozansky, L.; Sanderson, B.; Sato, N.; Shinohara, Y.; Stanford, T.; Stoimenow, A.; Takata, T.; Thurston, D.; Turaev, V.; Viro, O.; Willerton, S.; Yokota, Y. Problems on invariants of knots and 3-manifolds. arXiv:math/0406190 Preprint, arXiv:math/0406190 [math.GT] (2004). MSC: 20F36 57M25 57M27 57R56 13B25 17B10 17B37 18D10 20C08 20G42 22E99 41A60 46L37 57M05 57M50 57N10 57Q10 81T18 81T45 BibTeX Cite \textit{J. E. Andersen} et al., ``Problems on invariants of knots and 3-manifolds'', Preprint, arXiv:math/0406190 [math.GT] (2004) Full Text: arXiv
Liao, Shijun On a generalized Taylor theorem: a rational proof of the validity of the homotopy analysis method. (English) Zbl 1044.41019 Appl. Math. Mech., Engl. Ed. 24, No. 1, 53-60 (2003). Reviewer: László Leindler (Szeged) MSC: 41A58 26A06 PDFBibTeX XMLCite \textit{S. Liao}, Appl. Math. Mech., Engl. Ed. 24, No. 1, 53--60 (2003; Zbl 1044.41019) Full Text: DOI
Albrecht, Gudrun; Farouki, Rida T. Construction of \(C^ 2\) Pythagorean-hodograph interpolating splines by the homotopy method. (English) Zbl 0866.65008 Adv. Comput. Math. 5, No. 4, 417-442 (1996). Reviewer: E.Neuman (Carbondale) MSC: 65D07 65D05 41A15 PDFBibTeX XMLCite \textit{G. Albrecht} and \textit{R. T. Farouki}, Adv. Comput. Math. 5, No. 4, 417--442 (1996; Zbl 0866.65008) Full Text: DOI
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