Kováč, Juraj; Klika, Václav Liouville-Green approximation for linearly coupled systems: asymptotic analysis with applications to reaction-diffusion systems. (English) Zbl 1495.34073 Discrete Contin. Dyn. Syst., Ser. S 15, No. 9, 2553-2579 (2022). MSC: 34D05 34E20 35K57 92C15 PDFBibTeX XMLCite \textit{J. Kováč} and \textit{V. Klika}, Discrete Contin. Dyn. Syst., Ser. S 15, No. 9, 2553--2579 (2022; Zbl 1495.34073) Full Text: DOI arXiv
Balkanova, Olga; Frolenkov, Dmitry Moments of \(L\)-functions and the Liouville-Green method. (English) Zbl 1486.11071 J. Eur. Math. Soc. (JEMS) 23, No. 4, 1333-1380 (2021). MSC: 11F67 11F11 34E20 PDFBibTeX XMLCite \textit{O. Balkanova} and \textit{D. Frolenkov}, J. Eur. Math. Soc. (JEMS) 23, No. 4, 1333--1380 (2021; Zbl 1486.11071) Full Text: DOI arXiv
Balkanova, Olga; Bhowmik, Gautami; Frolenkov, Dmitry; Raulf, Nicole A mean value result for a product of \(\mathrm{GL}(2)\) and \(\mathrm{GL}(3)\) \(L\)-functions. (English) Zbl 1443.11075 Mathematika 65, No. 3, 743-762 (2019). MSC: 11F67 11F66 11F11 PDFBibTeX XMLCite \textit{O. Balkanova} et al., Mathematika 65, No. 3, 743--762 (2019; Zbl 1443.11075) Full Text: DOI arXiv
Spigler, Renato Asymptotic-numerical approximations for highly oscillatory second-order differential equations by the phase function method. (English) Zbl 1404.65059 J. Math. Anal. Appl. 463, No. 1, 318-344 (2018). MSC: 65L05 65L10 34B05 34A30 34C10 PDFBibTeX XMLCite \textit{R. Spigler}, J. Math. Anal. Appl. 463, No. 1, 318--344 (2018; Zbl 1404.65059) Full Text: DOI
Balkanova, Olga; Frolenkov, Dmitry The mean value of symmetric square \(L\)-functions. (English) Zbl 1445.11039 Algebra Number Theory 12, No. 1, 35-59 (2018). MSC: 11F66 33C05 34E05 34E20 PDFBibTeX XMLCite \textit{O. Balkanova} and \textit{D. Frolenkov}, Algebra Number Theory 12, No. 1, 35--59 (2018; Zbl 1445.11039) Full Text: DOI arXiv
Geronimo, Jeffrey S.; Smith, Dale T. Corrigendum to “WKB (Liouville-Green) analysis of second order difference equations and applications” [J. Approx. Theory 69 (1992) 269-301]. (English) Zbl 1301.41023 J. Approx. Theory 188, 69-70 (2014). MSC: 41A60 PDFBibTeX XMLCite \textit{J. S. Geronimo} and \textit{D. T. Smith}, J. Approx. Theory 188, 69--70 (2014; Zbl 1301.41023) Full Text: DOI
Daros, C. H. Liouville-Green approximation for Bleustein-Gulyaev waves in functionally graded materials. (English) Zbl 1347.74042 Eur. J. Mech., A, Solids 38, 129-137 (2013). MSC: 74J15 74G10 74A55 PDFBibTeX XMLCite \textit{C. H. Daros}, Eur. J. Mech., A, Solids 38, 129--137 (2013; Zbl 1347.74042) Full Text: DOI
Segura, Javier Computing the complex zeros of special functions. (English) Zbl 1271.65087 Numer. Math. 124, No. 4, 723-752 (2013). MSC: 65H05 65E05 33F05 33C10 34M10 34E20 34C10 PDFBibTeX XMLCite \textit{J. Segura}, Numer. Math. 124, No. 4, 723--752 (2013; Zbl 1271.65087) Full Text: DOI
Stepin, S. A. Asymptotic integration of nonoscillatory second-order differential equations. (English. Russian original) Zbl 1228.34073 Dokl. Math. 82, No. 2, 751-754 (2010); translation from Dokl. Akad. Nauk., Ross. Akad. Nauk. 434, No. 3, 315-318 (2010). Reviewer: Fei Xue (Hartford) MSC: 34D05 34E10 34C20 34A30 PDFBibTeX XMLCite \textit{S. A. Stepin}, Dokl. Math. 82, No. 2, 751--754 (2010; Zbl 1228.34073); translation from Dokl. Akad. Nauk., Ross. Akad. Nauk. 434, No. 3, 315--318 (2010) Full Text: DOI
Pinto, Manuel; Rivas, Cristóbal Generalized finite moments and Liouville-Green approximations. (English) Zbl 1165.34309 Math. Comput. Modelling 49, No. 1-2, 1-12 (2009). MSC: 34A45 PDFBibTeX XMLCite \textit{M. Pinto} and \textit{C. Rivas}, Math. Comput. Modelling 49, No. 1--2, 1--12 (2009; Zbl 1165.34309) Full Text: DOI
Spigler, Renato; Vianello, Marco Liouville-Green asymptotic approximation for a class of matrix differential equations and semi-discretized partial differential equations. (English) Zbl 1119.34004 J. Math. Anal. Appl. 325, No. 1, 69-89 (2007). Reviewer: Narahari Parhi (Bhubaneswar) MSC: 34A30 35K57 35L05 34A45 34E10 34D05 PDFBibTeX XMLCite \textit{R. Spigler} and \textit{M. Vianello}, J. Math. Anal. Appl. 325, No. 1, 69--89 (2007; Zbl 1119.34004) Full Text: DOI
El Karoui, Noureddine A rate of convergence result for the largest eigenvalue of complex white Wishart matrices. (English) Zbl 1108.62014 Ann. Probab. 34, No. 6, 2077-2117 (2006). MSC: 62E20 60F05 15B52 62H10 15A18 PDFBibTeX XMLCite \textit{N. El Karoui}, Ann. Probab. 34, No. 6, 2077--2117 (2006; Zbl 1108.62014) Full Text: DOI arXiv
Stanković, Bogoljub; Atanacković, Teodor M. On the lateral vibrations of an elastic rod with varying compressive force. (English) Zbl 1100.74031 Theor. Appl. Mech. (Belgrade) 31, No. 2, 135-151 (2004). Reviewer: Vojislav Marić (Novi Sad) MSC: 74H45 74K10 74H25 35Q72 PDFBibTeX XMLCite \textit{B. Stanković} and \textit{T. M. Atanacković}, Theor. Appl. Mech. (Belgrade) 31, No. 2, 135--151 (2004; Zbl 1100.74031) Full Text: DOI
Vu Hoang Linh On the high order asymptotic solution of certain wave equations. (English) Zbl 1057.34052 Miskolc Math. Notes 5, No. 1, 57-69 (2004). MSC: 34E05 34E20 34A30 PDFBibTeX XMLCite \textit{Vu Hoang Linh}, Miskolc Math. Notes 5, No. 1, 57--69 (2004; Zbl 1057.34052)
Gilbert, D. J.; Wood, A. D. Stokes’ phenomenon and the absolutely continuous spectrum of one-dimensional Schrödinger operators. (English) Zbl 1085.34069 J. Comput. Appl. Math. 171, No. 1-2, 247-264 (2004). MSC: 34M40 34B20 34L40 PDFBibTeX XMLCite \textit{D. J. Gilbert} and \textit{A. D. Wood}, J. Comput. Appl. Math. 171, No. 1--2, 247--264 (2004; Zbl 1085.34069) Full Text: DOI
Gatteschi, Luigi Asymptotics and bounds for the zeros of Laguerre polynomials: A survey. (English) Zbl 1008.65011 J. Comput. Appl. Math. 144, No. 1-2, 7-27 (2002). Reviewer: N.M.Temme (Amsterdam) MSC: 65D20 33C10 33C45 33F05 PDFBibTeX XMLCite \textit{L. Gatteschi}, J. Comput. Appl. Math. 144, No. 1--2, 7--27 (2002; Zbl 1008.65011) Full Text: DOI
Gabutti, Bruno; Gatteschi, Luigi New asymptotics for the zeros of Whittaker’s functions. (English) Zbl 0989.33005 Numer. Algorithms 28, No. 1-4, 159-170 (2001). Reviewer: Sven Ehrich (Neuherberg) MSC: 33C15 65D20 33C10 41A60 PDFBibTeX XMLCite \textit{B. Gabutti} and \textit{L. Gatteschi}, Numer. Algorithms 28, No. 1--4, 159--170 (2001; Zbl 0989.33005) Full Text: DOI
Baikov, V. A.; Khalique, C. M. Some invariant solutions for unsaturated flow models with plant root extraction. (English) Zbl 0989.35109 Quaest. Math. 24, No. 1, 9-19 (2001). Reviewer: Hu Chuangan (Tianjin) MSC: 35Q35 76S05 37K30 PDFBibTeX XMLCite \textit{V. A. Baikov} and \textit{C. M. Khalique}, Quaest. Math. 24, No. 1, 9--19 (2001; Zbl 0989.35109) Full Text: DOI
Elias, Uri; Gingold, Harry Asymptotic approximation for matrix differential equations and applications. (English) Zbl 0976.34049 Magalhães, L. (ed.) et al., International conference on differential equations. Papers from the conference, EQUADIFF 95, Lisboa, Portugal, July 24-29, 1995. Singapore: World Scientific. 316-321 (1998). MSC: 34E20 34C10 PDFBibTeX XMLCite \textit{U. Elias} and \textit{H. Gingold}, in: International conference on differential equations. Papers from the conference, EQUADIFF 95, Lisboa, Portugal, July 24--29, 1995. Singapore: World Scientific. 316--321 (1998; Zbl 0976.34049)
Spigler, Renato; Vianello, Marco A survey on the Liouville-Green (WKB) approximation for linear difference equation of the second order. (English) Zbl 0892.39018 Elaydi, S. (ed.) et al., Advances in difference equations. Proceedings of the 2nd international conference on difference equations, Veszprém, Hungary, August 7–11, 1995. Langhorne, PA: Gordon and Breach Science Publishers. 567-577 (1997). MSC: 39A12 39A10 34E20 PDFBibTeX XMLCite \textit{R. Spigler} and \textit{M. Vianello}, in: Advances in difference equations. Proceedings of the 2nd international conference on difference equations, Veszprém, Hungary, August 7--11, 1995. Langhorne, PA: Gordon and Breach Science Publishers. 567--577 (1997; Zbl 0892.39018)
Elias, U.; Gingold, H. Asymptotic approximation for matrix differential equations and applications. (English) Zbl 0879.34055 Differ. Integral Equ. 10, No. 1, 137-152 (1997). Reviewer: I.Rachůnková (Olomouc) MSC: 34E10 34C10 PDFBibTeX XMLCite \textit{U. Elias} and \textit{H. Gingold}, Differ. Integral Equ. 10, No. 1, 137--152 (1997; Zbl 0879.34055)
Mulholland, Anthony J.; Gomatam, Jagannathan The eikonal approximation to excitable reaction-diffusion systems: travelling non-planar wave fronts on the plane. (English) Zbl 0884.35062 Physica D 89, No. 3-4, 329-345 (1996). MSC: 35K57 35B35 PDFBibTeX XMLCite \textit{A. J. Mulholland} and \textit{J. Gomatam}, Physica D 89, No. 3--4, 329--345 (1996; Zbl 0884.35062) Full Text: DOI
Spigler, Renato; Vianello, Marco Discrete and continuous Liouville-Green-Olver approximations: A unified treatment via Volterra-Stieltjes integral equations. (English) Zbl 0791.39006 SIAM J. Math. Anal. 25, No. 2, 720-732 (1994). Reviewer: R.Spigler (Padova) MSC: 39A12 34E20 45D05 28A10 PDFBibTeX XMLCite \textit{R. Spigler} and \textit{M. Vianello}, SIAM J. Math. Anal. 25, No. 2, 720--732 (1994; Zbl 0791.39006) Full Text: DOI
Geronimo, Jeffrey S.; Smith, Dale T. WKB (Liouville-Green) analysis of second order difference equations and applications. (English) Zbl 0764.41030 J. Approximation Theory 69, No. 3, 269-301 (1992); corrigendum ibid. 188, 69-70 (2014). Reviewer: N.M.Temme (Amsterdam) MSC: 41A60 65L05 39A10 PDFBibTeX XMLCite \textit{J. S. Geronimo} and \textit{D. T. Smith}, J. Approx. Theory 69, No. 3, 269--301 (1992; Zbl 0764.41030) Full Text: DOI
Spigler, Renato; Vianello, Marco Liouville-Green approximations for a class of linear oscillatory difference equations of the second order. (English) Zbl 0726.39002 J. Comput. Appl. Math. (to appear). Reviewer: R.Spigler (Padova) MSC: 39A10 39A12 42C05 33C45 PDFBibTeX XML
Spigler, Renato; Vianello, Marco WKBJ-type approximation for finite moments perturbations of the differential equation \(y\)”=\(0\) and the analogous difference equation. (English) Zbl 0757.34045 J. Math. Anal. Appl. 169, No. 2, 437-452 (1992). MSC: 34E20 39A10 39A12 PDFBibTeX XMLCite \textit{R. Spigler} and \textit{M. Vianello}, J. Math. Anal. Appl. 169, No. 2, 437--452 (1992; Zbl 0757.34045) Full Text: DOI
Spigler, Renato; Vianello, Marco Liouville-Green approximations for a class of linear oscillatory difference equations of the second order. (English) Zbl 0749.39001 J. Comput. Appl. Math. 41, No. 1-2, 105-116 (1992). MSC: 39A10 39A12 42C05 33C45 PDFBibTeX XMLCite \textit{R. Spigler} and \textit{M. Vianello}, J. Comput. Appl. Math. 41, No. 1--2, 105--116 (1992; Zbl 0749.39001) Full Text: DOI
Spigler, Renato; Vianello, Marco WKBJ-type approximation for finite moments perturbations of the differential equation \(y''=0\) and the analogous difference equation. (English) Zbl 0723.34041 J. Math. Anal. Appl. (to appear). Reviewer: R.Spigler (Padova) MSC: 34E20 39A10 39A12 PDFBibTeX XML
Gingold, Harry; Hu, Jishan Transcendentally small reflection of waves for problems with/without turning points near infinity: A new uniform approach. (English) Zbl 0743.34061 J. Math. Phys. 32, No. 12, 3278-3284 (1991). MSC: 34E20 81Q15 PDFBibTeX XMLCite \textit{H. Gingold} and \textit{J. Hu}, J. Math. Phys. 32, No. 12, 3278--3284 (1991; Zbl 0743.34061) Full Text: DOI
Spigler, Renato; Vianello, Marco Global existence and uniqueness for the Kummer transformation problem subject to non-Cauchy data. (English) Zbl 0743.34043 Differ. Integral Equ. 4, No. 5, 991-1003 (1991). Reviewer: F.M.Ragab (Cairo) MSC: 34C20 34E20 34A34 34C10 PDFBibTeX XMLCite \textit{R. Spigler} and \textit{M. Vianello}, Differ. Integral Equ. 4, No. 5, 991--1003 (1991; Zbl 0743.34043)
Olver, F. Prudnikov, A. P. (ed.) Asymptotics and special functions. (Asimptotika i spetsial’nye funktsii). Transl. from the English by Yu. A. Brychkov. Transl. ed. by A. P. Prudnikov. (Asimptotika i spetsial’nye funktsii.) (Russian) Zbl 0712.41006 Moskva: Nauka. 528 p. (1990). MSC: 41A60 41-02 33-02 34-02 34E05 PDFBibTeX XMLCite \textit{F. Olver} and \textit{A. P. Prudnikov} (ed.), Asimptotika i spetsial'nye funktsii (Russian). Transl. from the English by Yu. A. Brychkov. Transl. ed. by A. P. Prudnikov. Moskva: Nauka (1990; Zbl 0712.41006)
Marić, Vojislav; Topmić, Miodrag On Liouville Green (WKB) approximation for second order linear differential equations. (English) Zbl 0723.34039 Differ. Integral Equ. 1, No. 3, 299-304 (1988). MSC: 34E05 34E20 PDFBibTeX XMLCite \textit{V. Marić} and \textit{M. Topmić}, Differ. Integral Equ. 1, No. 3, 299--304 (1988; Zbl 0723.34039)
Gingold, H. An invariant asymptotic formula for solutions of second-order linear ODE’s. (English) Zbl 0672.34051 Asymptotic Anal. 1, No. 4, 317-350 (1988). Reviewer: J.Kalas MSC: 34E05 34A30 34E20 PDFBibTeX XMLCite \textit{H. Gingold}, Asymptotic Anal. 1, No. 4, 317--350 (1988; Zbl 0672.34051)
Davies, E. B.; Harrell, Evans M. II Conformally flat Riemannian metrics, Schrödinger operators, and semiclassical approximation. (English) Zbl 0616.34020 J. Differ. Equations 66, 165-188 (1987). Reviewer: P.N.Bajaj MSC: 34L99 PDFBibTeX XMLCite \textit{E. B. Davies} and \textit{E. M. Harrell II}, J. Differ. Equations 66, 165--188 (1987; Zbl 0616.34020) Full Text: DOI
Smith, Donald R. Liouville-Green approximations via the Riccati transformation. (English) Zbl 0618.34011 J. Math. Anal. Appl. 116, 147-165 (1986). Reviewer: G.Caristi MSC: 34A45 34B05 PDFBibTeX XMLCite \textit{D. R. Smith}, J. Math. Anal. Appl. 116, 147--165 (1986; Zbl 0618.34011) Full Text: DOI
Nuttall, J. Asymptotics of generalized Jacobi polynomials. (English) Zbl 0585.41014 Constructive Approximation 2, 59-77 (1986). MSC: 41A21 42C05 33C45 PDFBibTeX XMLCite \textit{J. Nuttall}, Constr. Approx. 2, 59--77 (1986; Zbl 0585.41014) Full Text: DOI
Caliceti, E.; Grecchi, V.; Levoni, S.; Maioli, M. The exponential anharmonic oscillator and the Stieltjes continued fraction. (English) Zbl 0581.34020 Boll. Unione Mat. Ital., Suppl. 1985, No. 1, 55-69 (1985). Reviewer: P.K.Wong MSC: 34L99 34C15 40A15 81Q15 34E10 PDFBibTeX XMLCite \textit{E. Caliceti} et al., Boll. Unione Mat. Ital., Suppl. 1985, No. 1, 55--69 (1985; Zbl 0581.34020)
Hadid, S. Exponentially large estimates for solutions of systems of differential equations. (English) Zbl 0644.34013 Arab J. Math. 5, No. 1-2, 71-80 (1984). MSC: 34A45 PDFBibTeX XMLCite \textit{S. Hadid}, Arab J. Math. 5, No. 1--2, 71--80 (1984; Zbl 0644.34013)
Taylor, James G. Improved error bounds for the Liouville Green (or WKB) approximation. (English) Zbl 0499.34035 J. Math. Anal. Appl. 85, 79-89 (1982). MSC: 34E20 34B27 34A45 45E10 45G05 PDFBibTeX XMLCite \textit{J. G. Taylor}, J. Math. Anal. Appl. 85, 79--89 (1982; Zbl 0499.34035) Full Text: DOI
Gammel, J. L.; Nuttall, J. Note on generalized Jacobi polynomials. (English) Zbl 0491.41020 The Riemann problem, complete integrability and arithmetic applications, Proc. Semin., France and USA 1979-1980, Lect. Notes Math. 925, 258-270 (1982). MSC: 41A21 41A10 41A20 PDFBibTeX XML
Barrett, W. Mathieu functions of general order: connection formulae, base functions and asymptotic formulae. (English) Zbl 0452.33010 Philos. Trans. R. Soc. Lond., A 301, 75-162 (1981). MSC: 33E10 PDFBibTeX XMLCite \textit{W. Barrett}, Philos. Trans. R. Soc. Lond., Ser. A 301, 75--162 (1981; Zbl 0452.33010) Full Text: DOI
Olver, Frank W. J. The general connection-formula problem for linear differential equations of the second order. (English) Zbl 0494.34006 Singular perturbations and asymptotics, Proc. adv. Semin., Madison/ Wis. 1980, 317-343 (1980). MSC: 34A45 34A30 PDFBibTeX XML
Gavalas, G. R.; Yortsos, Y. C. Short-time asymptotic solutions of the heat conduction equation with spatially varying coefficients. (English) Zbl 0455.35069 J. Inst. Math. Appl. 26, 209-219 (1980). MSC: 35K05 35B40 PDFBibTeX XMLCite \textit{G. R. Gavalas} and \textit{Y. C. Yortsos}, J. Inst. Math. Appl. 26, 209--219 (1980; Zbl 0455.35069) Full Text: DOI
Radmore, P. M. The Schrödinger equation with an anharmonic oscillator potential. (English) Zbl 0428.35022 J. Phys. A 13, 173-179 (1980). MSC: 35J10 35Q99 81Q05 34A45 34L99 35P05 PDFBibTeX XMLCite \textit{P. M. Radmore}, J. Phys. A, Math. Gen. 13, 173--179 (1980; Zbl 0428.35022) Full Text: DOI