Zhang, Xiaolong; Boyd, John P. Exact solutions to a nonlinear partial differential equation: the Product-of-Curvatures Poisson \((u_{x x} u_{y y} = 1)\). (English) Zbl 07472414 J. Comput. Appl. Math. 406, Article ID 113866, 18 p. (2022). MSC: 33F05 42A10 41A50 PDF BibTeX XML Cite \textit{X. Zhang} and \textit{J. P. Boyd}, J. Comput. Appl. Math. 406, Article ID 113866, 18 p. (2022; Zbl 07472414) Full Text: DOI OpenURL
Faugaret, Antoine; Duguet, Yohann; Fraigneau, Yann; Martin Witkowski, Laurent A simple model for arbitrary pollution effects on rotating free-surface flows. (English) Zbl 07469311 J. Fluid Mech. 935, Paper No. A2, 27 p. (2022). MSC: 76-XX PDF BibTeX XML Cite \textit{A. Faugaret} et al., J. Fluid Mech. 935, Paper No. A2, 27 p. (2022; Zbl 07469311) Full Text: DOI OpenURL
De Marchi, Stefano; Elefante, Giacomo; Marchetti, Francesco On \((\beta,\gamma)\)-Chebyshev functions and points of the interval. (English) Zbl 1482.41001 J. Approx. Theory 271, Article ID 105634, 17 p. (2021). Reviewer: Marcel G. de Bruin (Heemstede) MSC: 41A05 33C45 42C05 PDF BibTeX XML Cite \textit{S. De Marchi} et al., J. Approx. Theory 271, Article ID 105634, 17 p. (2021; Zbl 1482.41001) Full Text: DOI arXiv OpenURL
Awonusika, Richard Olu On Jacobi polynomials and fractional spectral functions on compact symmetric spaces. (English) Zbl 07383717 J. Anal. 29, No. 3, 987-1024 (2021). MSC: 33D15 33D45 PDF BibTeX XML Cite \textit{R. O. Awonusika}, J. Anal. 29, No. 3, 987--1024 (2021; Zbl 07383717) Full Text: DOI OpenURL
Feng, Hongsong; Long, Guangqing; Zhao, Shan FFT-based high order central difference schemes for Poisson’s equation with staggered boundaries. (English) Zbl 1456.65140 J. Sci. Comput. 86, No. 1, Paper No. 7, 25 p. (2021). MSC: 65N06 65T50 65N85 35J05 PDF BibTeX XML Cite \textit{H. Feng} et al., J. Sci. Comput. 86, No. 1, Paper No. 7, 25 p. (2021; Zbl 1456.65140) Full Text: DOI OpenURL
Feng, Hongsong; Zhao, Shan FFT-based high order central difference schemes for three-dimensional Poisson’s equation with various types of boundary conditions. (English) Zbl 1436.65159 J. Comput. Phys. 410, Article ID 109391, 23 p. (2020). MSC: 65N06 65T50 35J05 PDF BibTeX XML Cite \textit{H. Feng} and \textit{S. Zhao}, J. Comput. Phys. 410, Article ID 109391, 23 p. (2020; Zbl 1436.65159) Full Text: DOI OpenURL
Nitti, Alessandro; Kiendl, Josef; Reali, Alessandro; de Tullio, Marco D. An immersed-boundary/isogeometric method for fluid-structure interaction involving thin shells. (English) Zbl 1442.74121 Comput. Methods Appl. Mech. Eng. 364, Article ID 112977, 34 p. (2020). MSC: 74K25 65D07 74S05 65M60 74F10 PDF BibTeX XML Cite \textit{A. Nitti} et al., Comput. Methods Appl. Mech. Eng. 364, Article ID 112977, 34 p. (2020; Zbl 1442.74121) Full Text: DOI OpenURL
Chen, Sheng; Shen, Jie; Zhang, Zhimin; Zhou, Zhi A spectrally accurate approximation to subdiffusion equations using the log orthogonal functions. (English) Zbl 1434.65291 SIAM J. Sci. Comput. 42, No. 2, A849-A877 (2020). MSC: 65N35 65E05 65M70 41A05 41A10 41A25 35R11 33C45 65N30 PDF BibTeX XML Cite \textit{S. Chen} et al., SIAM J. Sci. Comput. 42, No. 2, A849--A877 (2020; Zbl 1434.65291) Full Text: DOI OpenURL
Chen, Sheng; Shen, Jie An efficient and accurate numerical method for the spectral fractional Laplacian equation. (English) Zbl 1433.65235 J. Sci. Comput. 82, No. 1, Paper No. 17, 25 p. (2020). MSC: 65M70 65N35 41A05 41A10 41A25 35R11 26A33 PDF BibTeX XML Cite \textit{S. Chen} and \textit{J. Shen}, J. Sci. Comput. 82, No. 1, Paper No. 17, 25 p. (2020; Zbl 1433.65235) Full Text: DOI OpenURL
Lee, Kiseok Chebyshev collocation method for the constant mobility Cahn-Hilliard equation in a square domain. (English) Zbl 1433.65242 Appl. Math. Comput. 370, Article ID 124931, 12 p. (2020). MSC: 65M70 35K35 35K55 82C26 65M12 65M15 PDF BibTeX XML Cite \textit{K. Lee}, Appl. Math. Comput. 370, Article ID 124931, 12 p. (2020; Zbl 1433.65242) Full Text: DOI OpenURL
Shen, Jie; Sheng, Chang-Tao An efficient space-time method for time fractional diffusion equation. (English) Zbl 1466.65214 J. Sci. Comput. 81, No. 2, 1088-1110 (2019). MSC: 65N35 26A33 35R11 65N15 PDF BibTeX XML Cite \textit{J. Shen} and \textit{C.-T. Sheng}, J. Sci. Comput. 81, No. 2, 1088--1110 (2019; Zbl 1466.65214) Full Text: DOI OpenURL
Mao, Zhiping; Shen, Jie Hermite spectral methods for fractional PDEs in unbounded domains. (English) Zbl 1373.65075 SIAM J. Sci. Comput. 39, No. 5, A1928-A1950 (2017). MSC: 65M70 65N35 35Q55 35R11 65M15 65N15 65M60 65N30 PDF BibTeX XML Cite \textit{Z. Mao} and \textit{J. Shen}, SIAM J. Sci. Comput. 39, No. 5, A1928--A1950 (2017; Zbl 1373.65075) Full Text: DOI OpenURL
Mao, Zhiping; Shen, Jie Efficient spectral-Galerkin methods for fractional partial differential equations with variable coefficients. (English) Zbl 1352.65395 J. Comput. Phys. 307, 243-261 (2016). MSC: 65M70 65M60 35R11 35S15 PDF BibTeX XML Cite \textit{Z. Mao} and \textit{J. Shen}, J. Comput. Phys. 307, 243--261 (2016; Zbl 1352.65395) Full Text: DOI OpenURL
Townsend, Alex; Olver, Sheehan The automatic solution of partial differential equations using a global spectral method. (English) Zbl 1352.65579 J. Comput. Phys. 299, 106-123 (2015). MSC: 65N35 PDF BibTeX XML Cite \textit{A. Townsend} and \textit{S. Olver}, J. Comput. Phys. 299, 106--123 (2015; Zbl 1352.65579) Full Text: DOI arXiv OpenURL
Isik, Osman Rasit; Sezer, Mehmet; Guney, Zekeriya Bernstein series solution of linear second-order partial differential equations with mixed conditions. (English) Zbl 1291.65350 Math. Methods Appl. Sci. 37, No. 5, 609-619 (2014). Reviewer: Constantin Popa (Constanţa) MSC: 65N35 35J25 65N15 PDF BibTeX XML Cite \textit{O. R. Isik} et al., Math. Methods Appl. Sci. 37, No. 5, 609--619 (2014; Zbl 1291.65350) Full Text: DOI OpenURL
Çelik, İbrahim Haar wavelet approximation for magnetohydrodynamic flow equations. (English) Zbl 1271.76377 Appl. Math. Modelling 37, No. 6, 3894-3902 (2013). MSC: 76W05 65T60 PDF BibTeX XML Cite \textit{İ. Çelik}, Appl. Math. Modelling 37, No. 6, 3894--3902 (2013; Zbl 1271.76377) Full Text: DOI Link OpenURL
Bouloumou, Ouafa; Serre, Eric; Bontoux, Patrick; Fröhlich, Jochen A 3D pseudo-spectral low Mach-number solver for buoyancy driven flows with large temperature differences. (English) Zbl 1365.76207 Comput. Fluids 66, 107-120 (2012). MSC: 76M22 76R10 76D05 PDF BibTeX XML Cite \textit{O. Bouloumou} et al., Comput. Fluids 66, 107--120 (2012; Zbl 1365.76207) Full Text: DOI OpenURL
Doha, Eid H.; Bhrawy, Ali H. An efficient direct solver for multidimensional elliptic Robin boundary value problems using a Legendre spectral-Galerkin method. (English) Zbl 1252.65194 Comput. Math. Appl. 64, No. 4, 558-571 (2012). MSC: 65N35 PDF BibTeX XML Cite \textit{E. H. Doha} and \textit{A. H. Bhrawy}, Comput. Math. Appl. 64, No. 4, 558--571 (2012; Zbl 1252.65194) Full Text: DOI OpenURL
Chen, Feng; Shen, Jie Efficient spectral-Galerkin methods for systems of coupled second-order equations and their applications. (English) Zbl 1250.65138 J. Comput. Phys. 231, No. 15, 5016-5028 (2012). MSC: 65N30 65N35 35J25 65Y20 35K55 65M60 65M70 PDF BibTeX XML Cite \textit{F. Chen} and \textit{J. Shen}, J. Comput. Phys. 231, No. 15, 5016--5028 (2012; Zbl 1250.65138) Full Text: DOI OpenURL
Horng, Tzyy-Leng; Teng, Chun-Hao An error minimized pseudospectral penalty direct Poisson solver. (English) Zbl 1242.65248 J. Comput. Phys. 231, No. 6, 2498-2509 (2012). MSC: 65N35 35J05 65N15 PDF BibTeX XML Cite \textit{T.-L. Horng} and \textit{C.-H. Teng}, J. Comput. Phys. 231, No. 6, 2498--2509 (2012; Zbl 1242.65248) Full Text: DOI OpenURL
Chen, Yanping; Xia, Nianshi; Yi, Nianyu A Legendre Galerkin spectral method for optimal control problems. (English) Zbl 1256.49035 J. Syst. Sci. Complex. 24, No. 4, 663-671 (2011). MSC: 49M25 35Q93 PDF BibTeX XML Cite \textit{Y. Chen} et al., J. Syst. Sci. Complex. 24, No. 4, 663--671 (2011; Zbl 1256.49035) Full Text: DOI OpenURL
Bialecki, Bernard; Fairweather, Graeme; Karageorghis, Andreas Matrix decomposition algorithms for elliptic boundary value problems: A survey. (English) Zbl 1208.65036 Numer. Algorithms 56, No. 2, 253-295 (2011). MSC: 65F05 PDF BibTeX XML Cite \textit{B. Bialecki} et al., Numer. Algorithms 56, No. 2, 253--295 (2011; Zbl 1208.65036) Full Text: DOI OpenURL
Bhrawy, A. H.; El-Soubhy, S. I. Jacobi spectral Galerkin method for the integrated forms of second-order differential equations. (English) Zbl 1204.65132 Appl. Math. Comput. 217, No. 6, 2684-2697 (2010). Reviewer: Calin Ioan Gheorghiu (Cluj-Napoca) MSC: 65N30 65N35 35J25 35J05 PDF BibTeX XML Cite \textit{A. H. Bhrawy} and \textit{S. I. El-Soubhy}, Appl. Math. Comput. 217, No. 6, 2684--2697 (2010; Zbl 1204.65132) Full Text: DOI OpenURL
Li, Ben-Wen; Tian, Shuai; Sun, Ya-Song; Hu, Zhang-Mao Schur-decomposition for 3D matrix equations and its application in solving radiative discrete ordinates equations discretized by Chebyshev collocation spectral method. (English) Zbl 1183.65152 J. Comput. Phys. 229, No. 4, 1198-1212 (2010). MSC: 65N35 PDF BibTeX XML Cite \textit{B.-W. Li} et al., J. Comput. Phys. 229, No. 4, 1198--1212 (2010; Zbl 1183.65152) Full Text: DOI OpenURL
Doha, E. H.; Ahmed, H. M.; El-Soubhy, S. I. Explicit formulae for the coefficients of integrated expansions of Laguerre and Hermite polynomials and their integrals. (English) Zbl 1169.42314 Integral Transforms Spec. Funct. 20, No. 7-8, 491-503 (2009). MSC: 42C10 65L50 65L10 PDF BibTeX XML Cite \textit{E. H. Doha} et al., Integral Transforms Spec. Funct. 20, No. 7--8, 491--503 (2009; Zbl 1169.42314) Full Text: DOI OpenURL
Akyüz-Dascioglu, Aysegül Chebyshev polynomial approximation for high-order partial differential equations with complicated conditions. (English) Zbl 1167.65067 Numer. Methods Partial Differ. Equations 25, No. 3, 610-621 (2009). Reviewer: Adrian Carabineanu (Bucureşti) MSC: 65N35 35G15 PDF BibTeX XML Cite \textit{A. Akyüz-Dascioglu}, Numer. Methods Partial Differ. Equations 25, No. 3, 610--621 (2009; Zbl 1167.65067) Full Text: DOI OpenURL
Boyd, John P. Large-degree asymptotics and exponential asymptotics for Fourier, Chebyshev and Hermite coefficients and Fourier transforms. (English) Zbl 1163.42001 J. Eng. Math. 63, No. 2-4, 355-399 (2009). Reviewer: Marcel G. de Bruin (Haarlem) MSC: 42-02 41A60 PDF BibTeX XML Cite \textit{J. P. Boyd}, J. Eng. Math. 63, No. 2--4, 355--399 (2009; Zbl 1163.42001) Full Text: DOI OpenURL
Julien, Keith; Watson, Mike Efficient multi-dimensional solution of PDEs using Chebyshev spectral methods. (English) Zbl 1166.65325 J. Comput. Phys. 228, No. 5, 1480-1503 (2009). MSC: 65F05 65F50 65N35 65N22 PDF BibTeX XML Cite \textit{K. Julien} and \textit{M. Watson}, J. Comput. Phys. 228, No. 5, 1480--1503 (2009; Zbl 1166.65325) Full Text: DOI OpenURL
Nguyen, S.; Delcarte, C.; Kasperski, G. On the regularity of some thermocapillary convection models. (English) Zbl 1151.76585 Eur. J. Mech., B, Fluids 27, No. 6, 771-784 (2008). MSC: 76R10 76D45 80A20 PDF BibTeX XML Cite \textit{S. Nguyen} et al., Eur. J. Mech., B, Fluids 27, No. 6, 771--784 (2008; Zbl 1151.76585) Full Text: DOI OpenURL
Ahmed, H. M.; El-Soubhy, S. I. Recurrences and explicit formulae for the expansion and connection coefficients in series of ordinary Bessel polynomials. (English) Zbl 1152.33005 Appl. Math. Comput. 199, No. 2, 482-493 (2008). Reviewer: Pushpa N. Rathie (Brasilia) MSC: 33C45 PDF BibTeX XML Cite \textit{H. M. Ahmed} and \textit{S. I. El-Soubhy}, Appl. Math. Comput. 199, No. 2, 482--493 (2008; Zbl 1152.33005) Full Text: DOI OpenURL
Elbarbary, Elsayed M. E. Efficient Chebyshev-Petrov-Galerkin method for solving second-order equations. (English) Zbl 1136.65106 J. Sci. Comput. 34, No. 2, 113-126 (2008). MSC: 65N30 35J25 65F50 65Y20 PDF BibTeX XML Cite \textit{E. M. E. Elbarbary}, J. Sci. Comput. 34, No. 2, 113--126 (2008; Zbl 1136.65106) Full Text: DOI OpenURL
Doha, E. H.; Bhrawy, A. H. Efficient spectral-Galerkin algorithms for direct solution of the integrated forms of second-order equations using ultraspherical polynomials. (English) Zbl 1138.65104 ANZIAM J. 48, No. 3, 361-386 (2007). Reviewer: Ariadna Lucia Pletea (Iaşi) MSC: 65N35 35J05 PDF BibTeX XML Cite \textit{E. H. Doha} and \textit{A. H. Bhrawy}, ANZIAM J. 48, No. 3, 361--386 (2007; Zbl 1138.65104) Full Text: DOI OpenURL
Güray, E.; Tarman, H. I. Thermal convection in the presence of a vertical magnetic field. (English) Zbl 1140.76493 Acta Mech. 194, No. 1-4, 33-46 (2007). MSC: 76W05 76R10 76M22 80A20 PDF BibTeX XML Cite \textit{E. Güray} and \textit{H. I. Tarman}, Acta Mech. 194, No. 1--4, 33--46 (2007; Zbl 1140.76493) Full Text: DOI OpenURL
Kwan, Yuen-Yick; Shen, Jie An efficient direct parallel spectral-element solver for separable elliptic problems. (English) Zbl 1123.65116 J. Comput. Phys. 225, No. 2, 1721-1735 (2007). MSC: 65N35 65Y05 35J05 PDF BibTeX XML Cite \textit{Y.-Y. Kwan} and \textit{J. Shen}, J. Comput. Phys. 225, No. 2, 1721--1735 (2007; Zbl 1123.65116) Full Text: DOI Link OpenURL
Jun, Se-Ran; Kang, Sungkwon; Kwon, Yong-Hoon A direct solver for the Legendre tau approximation for the two-dimensional Poisson problem. (English) Zbl 1115.65121 J. Appl. Math. Comput. 23, No. 1-2, 25-42 (2007). Reviewer: Wilhelm Heinrichs (Essen) MSC: 65N35 35J05 65F15 65N12 PDF BibTeX XML Cite \textit{S.-R. Jun} et al., J. Appl. Math. Comput. 23, No. 1--2, 25--42 (2007; Zbl 1115.65121) Full Text: DOI OpenURL
Hu, Hsin-Yun; Li, Zi-Cai Combinations of collocation and finite-element methods for Poisson’s equation. (English) Zbl 1134.65083 Comput. Math. Appl. 51, No. 12, 1831-1853 (2006). MSC: 65N35 65N30 65N12 35J05 PDF BibTeX XML Cite \textit{H.-Y. Hu} and \textit{Z.-C. Li}, Comput. Math. Appl. 51, No. 12, 1831--1853 (2006; Zbl 1134.65083) Full Text: DOI OpenURL
Doha, E. H.; Bhrawy, A. H. Efficient spectral-Galerkin algorithms for direct solution for second-order differential equations using Jacobi polynomials. (English) Zbl 1103.65119 Numer. Algorithms 42, No. 2, 137-164 (2006). Reviewer: Calin Ioan Gheorghiu (Cluj-Napoca) MSC: 65N35 65F05 35J05 65F35 PDF BibTeX XML Cite \textit{E. H. Doha} and \textit{A. H. Bhrawy}, Numer. Algorithms 42, No. 2, 137--164 (2006; Zbl 1103.65119) Full Text: DOI OpenURL
Hill, A. A.; Straughan, B. A Legendre spectral element method for eigenvalues in hydrodynamic stability. (English) Zbl 1092.65065 J. Comput. Appl. Math. 193, No. 1, 363-381 (2006). MSC: 65L15 34L16 76S05 76E20 PDF BibTeX XML Cite \textit{A. A. Hill} and \textit{B. Straughan}, J. Comput. Appl. Math. 193, No. 1, 363--381 (2006; Zbl 1092.65065) Full Text: DOI OpenURL
Doha, E. H.; Ahmed, H. M. On the coefficients of integrated expansions of Bessel polynomials. (English) Zbl 1076.42021 J. Comput. Appl. Math. 187, No. 1, 58-71 (2006). MSC: 42C10 33C45 65L50 65L10 PDF BibTeX XML Cite \textit{E. H. Doha} and \textit{H. M. Ahmed}, J. Comput. Appl. Math. 187, No. 1, 58--71 (2006; Zbl 1076.42021) Full Text: DOI OpenURL
Speetjens, M. F. M.; Clercx, H. J. H. A spectral solver for the Navier-Stokes equations in the velocity-vorticity formulation. (English) Zbl 1184.76774 Int. J. Comput. Fluid Dyn. 19, No. 3, 191-209 (2005). MSC: 76M22 76D05 PDF BibTeX XML Cite \textit{M. F. M. Speetjens} and \textit{H. J. H. Clercx}, Int. J. Comput. Fluid Dyn. 19, No. 3, 191--209 (2005; Zbl 1184.76774) Full Text: DOI OpenURL
Barbosa, E.; Daube, O. A finite difference method for 3D incompressible flows in cylindrical coordinates. (English) Zbl 1134.76404 Comput. Fluids 34, No. 8, 950-971 (2005). MSC: 76M20 76D05 65M06 PDF BibTeX XML Cite \textit{E. Barbosa} and \textit{O. Daube}, Comput. Fluids 34, No. 8, 950--971 (2005; Zbl 1134.76404) Full Text: DOI Link OpenURL
Doha, E. H.; Abd-Elhameed, W. M. Accurate spectral solutions for the parabolic and elliptic partial differential equations by the ultraspherical tau method. (English) Zbl 1071.65136 J. Comput. Appl. Math. 181, No. 1, 24-45 (2005). MSC: 65M70 65N35 35C10 42C10 PDF BibTeX XML Cite \textit{E. H. Doha} and \textit{W. M. Abd-Elhameed}, J. Comput. Appl. Math. 181, No. 1, 24--45 (2005; Zbl 1071.65136) Full Text: DOI OpenURL
Albensoeder, S.; Kuhlmann, H. C. Accurate three-dimensional lid-driven cavity flow. (English) Zbl 1121.76366 J. Comput. Phys. 206, No. 2, 536-558 (2005). MSC: 76M25 65M70 PDF BibTeX XML Cite \textit{S. Albensoeder} and \textit{H. C. Kuhlmann}, J. Comput. Phys. 206, No. 2, 536--558 (2005; Zbl 1121.76366) Full Text: DOI OpenURL
Ismail, I. A.; Ismail, G.; Sedqi, A. M. A computational method for solving the branched channel flow problem. (English) Zbl 1102.76058 Appl. Math. Comput. 161, No. 1, 19-34 (2005). MSC: 76M40 76M22 76D05 PDF BibTeX XML Cite \textit{I. A. Ismail} et al., Appl. Math. Comput. 161, No. 1, 19--34 (2005; Zbl 1102.76058) Full Text: DOI OpenURL
Nguyen, S.; Delcarte, C. A spectral collocation method to solve Helmholtz problems with boundary conditions involving mixed tangential and normal derivatives. (English) Zbl 1055.65134 J. Comput. Phys. 200, No. 1, 34-49 (2004). MSC: 65N35 35J05 76M22 76S05 PDF BibTeX XML Cite \textit{S. Nguyen} and \textit{C. Delcarte}, J. Comput. Phys. 200, No. 1, 34--49 (2004; Zbl 1055.65134) Full Text: DOI OpenURL
Botella, Olivier; Shariff, Karim B-spline methods in fluid dynamics. (English) Zbl 1115.76382 Int. J. Comput. Fluid Dyn. 17, No. 2, 133-149 (2003). MSC: 76M25 76D05 PDF BibTeX XML Cite \textit{O. Botella} and \textit{K. Shariff}, Int. J. Comput. Fluid Dyn. 17, No. 2, 133--149 (2003; Zbl 1115.76382) Full Text: DOI OpenURL
Xin, Guojun; Chow, W. K.; Liu, Shida Windows and routes to chaos in mixed convection in confined spaces. (English) Zbl 1038.76042 Chaos Solitons Fractals 15, No. 3, 543-558 (2003). MSC: 76R05 37N10 76R10 76M25 PDF BibTeX XML Cite \textit{G. Xin} et al., Chaos Solitons Fractals 15, No. 3, 543--558 (2003; Zbl 1038.76042) Full Text: DOI OpenURL
Doha, E. H. Explicit formulae for the coefficients of integrated expansions of Jacobi polynomials and their integrals. (English) Zbl 1051.33004 Integral Transforms Spec. Funct. 14, No. 1, 69-86 (2003). Reviewer: Ravi N. Kalia (St. Cloud) MSC: 33C45 42C10 PDF BibTeX XML Cite \textit{E. H. Doha}, Integral Transforms Spec. Funct. 14, No. 1, 69--86 (2003; Zbl 1051.33004) Full Text: DOI OpenURL
Auteri, F.; Parolini, N.; Quartapelle, L. Essential imposition of Neumann condition in Galerkin–Legendre elliptic solvers. (English) Zbl 1017.65093 J. Comput. Phys. 185, No. 2, 427-444 (2003). MSC: 65N35 35J05 PDF BibTeX XML Cite \textit{F. Auteri} et al., J. Comput. Phys. 185, No. 2, 427--444 (2003; Zbl 1017.65093) Full Text: DOI OpenURL
Daube, O.; Le Quéré, P. Numerical investigation of the first bifurcation for the flow in a rotor-stator cavity of radial aspect ratio 10. (English) Zbl 1004.76060 Comput. Fluids 31, No. 4-7, 481-494 (2002). MSC: 76M20 76E07 76U05 PDF BibTeX XML Cite \textit{O. Daube} and \textit{P. Le Quéré}, Comput. Fluids 31, No. 4--7, 481--494 (2002; Zbl 1004.76060) Full Text: DOI OpenURL
Helal, M. A. A Chebyshev spectral method for solving Korteweg-de Vries equation with hydrodynamical application. (English) Zbl 1017.65080 Chaos Solitons Fractals 12, No. 5, 943-950 (2001). MSC: 65M70 35Q53 76B15 76M22 PDF BibTeX XML Cite \textit{M. A. Helal}, Chaos Solitons Fractals 12, No. 5, 943--950 (2001; Zbl 1017.65080) Full Text: DOI OpenURL
El-Hawary, H. M. Double ultraspherical solution of eigenvalue problems for partial differential equations. (English) Zbl 1007.65089 Int. J. Comput. Math. 78, No. 2, 289-301 (2001). MSC: 65N25 65N35 35P15 PDF BibTeX XML Cite \textit{H. M. El-Hawary}, Int. J. Comput. Math. 78, No. 2, 289--301 (2001; Zbl 1007.65089) Full Text: DOI OpenURL
Doha, E. H.; Al-Kholi, F. M. R. An efficient double Legendre spectral method for parabolic and elliptic partial differential equations. (English) Zbl 1004.65101 Int. J. Comput. Math. 78, No. 3, 413-432 (2001). MSC: 65M70 65N35 35J05 35K05 PDF BibTeX XML Cite \textit{E. H. Doha} and \textit{F. M. R. Al-Kholi}, Int. J. Comput. Math. 78, No. 3, 413--432 (2001; Zbl 1004.65101) Full Text: DOI OpenURL
Auteri, F.; Quartapelle, L. Galerkin-Legendre spectral method for the 3D Helmholtz equation. (English) Zbl 0959.65130 J. Comput. Phys. 161, No. 2, 454-483 (2000). Reviewer: Calin Ioan Gheorghiu (Cluj-Napoca) MSC: 65N35 35J05 65F05 PDF BibTeX XML Cite \textit{F. Auteri} and \textit{L. Quartapelle}, J. Comput. Phys. 161, No. 2, 454--483 (2000; Zbl 0959.65130) Full Text: DOI OpenURL
Chen, Heli; Su, Yuhong; Shizgal, Bernie D. A direct spectral collocation Poisson solver in polar and cylindrical coordinates. (English) Zbl 0951.65125 J. Comput. Phys. 160, No. 2, 453-469 (2000). Reviewer: Gerald W.Hedstrom (Pleasanton) MSC: 65N35 35J05 PDF BibTeX XML Cite \textit{H. Chen} et al., J. Comput. Phys. 160, No. 2, 453--469 (2000; Zbl 0951.65125) Full Text: DOI OpenURL
Mittal, Rajat A Fourier-Chebyshev spectral collocation method for simulating flow past spheres and spheroids. (English) Zbl 0957.76060 Int. J. Numer. Methods Fluids 30, No. 7, 921-937 (1999). MSC: 76M22 76D05 76D25 PDF BibTeX XML Cite \textit{R. Mittal}, Int. J. Numer. Methods Fluids 30, No. 7, 921--937 (1999; Zbl 0957.76060) Full Text: DOI OpenURL
Boyd, John P.; Flyer, Natasha Compatibility conditions for time-dependent partial differential equations and the rate of convergence of Chebyshev and Fourier spectral methods. (English) Zbl 0932.65109 Comput. Methods Appl. Mech. Eng. 175, No. 3-4, 281-309 (1999). Reviewer: W.Heinrichs (Essen) MSC: 65M70 65M12 35K55 PDF BibTeX XML Cite \textit{J. P. Boyd} and \textit{N. Flyer}, Comput. Methods Appl. Mech. Eng. 175, No. 3--4, 281--309 (1999; Zbl 0932.65109) Full Text: DOI OpenURL
Auteri, F.; Quartapelle, L. Galerkin spectral method for the vorticity and stream function equations. (English) Zbl 0934.76065 J. Comput. Phys. 149, No. 2, 306-332 (1999). MSC: 76M22 76D05 PDF BibTeX XML Cite \textit{F. Auteri} and \textit{L. Quartapelle}, J. Comput. Phys. 149, No. 2, 306--332 (1999; Zbl 0934.76065) Full Text: DOI OpenURL
Hugues, Sandrine; Randriamampianina, Anthony An improved projection scheme applied to pseudospectral methods for the incompressible Navier-Stokes equations. (English) Zbl 0932.76065 Int. J. Numer. Methods Fluids 28, No. 3, 501-521 (1998). MSC: 76M22 76D05 65M70 PDF BibTeX XML Cite \textit{S. Hugues} and \textit{A. Randriamampianina}, Int. J. Numer. Methods Fluids 28, No. 3, 501--521 (1998; Zbl 0932.76065) Full Text: DOI OpenURL
Garba, A. A mixed spectral/wavelet method for the solution of the Stokes problem. (English) Zbl 0926.76083 J. Comput. Phys. 145, No. 1, 297-315 (1998). MSC: 76M22 76D07 65M70 PDF BibTeX XML Cite \textit{A. Garba}, J. Comput. Phys. 145, No. 1, 297--315 (1998; Zbl 0926.76083) Full Text: DOI OpenURL
Bade, François; Haldenwang, Pierre High order scheme for thermally driven flows in an open channel. (English) Zbl 0912.76039 Comput. Fluids 27, No. 2, 273-290 (1998). MSC: 76M20 76D05 80A20 PDF BibTeX XML Cite \textit{F. Bade} and \textit{P. Haldenwang}, Comput. Fluids 27, No. 2, 273--290 (1998; Zbl 0912.76039) Full Text: DOI OpenURL
Nakamura, Yukio Spatio-temporal dynamics of forced periodic flows in a confined domain. (English) Zbl 1185.76640 Phys. Fluids 9, No. 11, 3275-3287 (1997). MSC: 76E99 PDF BibTeX XML Cite \textit{Y. Nakamura}, Phys. Fluids 9, No. 11, 3275--3287 (1997; Zbl 1185.76640) Full Text: DOI OpenURL
Clercx, H. J. H. A spectral solver for the Navier-Stokes equations in the velocity-vorticity formulation for flows with two nonperiodic directions. (English) Zbl 0904.76058 J. Comput. Phys. 137, No. 1, 186-211 (1997). Reviewer: W.Heinrichs (Essen) MSC: 76M25 76D05 65M70 PDF BibTeX XML Cite \textit{H. J. H. Clercx}, J. Comput. Phys. 137, No. 1, 186--211 (1997; Zbl 0904.76058) Full Text: DOI OpenURL
Dongarra, J. J.; Straughan, B.; Walker, D. W. Chebyshev tau-QZ algorithm methods for calculating spectra of hydrodynamic stability problems. (English) Zbl 0867.76025 Appl. Numer. Math. 22, No. 4, 399-434 (1996). Reviewer: V.Burjan (Praha) MSC: 76E05 65L15 PDF BibTeX XML Cite \textit{J. J. Dongarra} et al., Appl. Numer. Math. 22, No. 4, 399--434 (1996; Zbl 0867.76025) Full Text: DOI OpenURL
Crespo Del Arco, E.; Maubert, P.; Randriamampianina, A.; Bontoux, P. Spatio-temporal behaviour in a rotating annulus with a source-sink flow. (English) Zbl 0890.76059 J. Fluid Mech. 328, 271-296 (1996). MSC: 76M25 76U05 76E99 37D45 PDF BibTeX XML Cite \textit{E. Crespo Del Arco} et al., J. Fluid Mech. 328, 271--296 (1996; Zbl 0890.76059) Full Text: DOI OpenURL
Xin, Shihe; Le Quéré, Patrick Direct numerical simulations of two-dimensional chaotic natural convection in a differentially heated cavity of aspect ratio 4. (English) Zbl 0850.76664 J. Fluid Mech. 304, 87-118 (1995). MSC: 76R10 76M25 76M20 PDF BibTeX XML Cite \textit{S. Xin} and \textit{P. Le Quéré}, J. Fluid Mech. 304, 87--118 (1995; Zbl 0850.76664) Full Text: DOI OpenURL
Yang, Henry H.; Shizgal, Bernie Chebyshev pseudospectral multi-domain technique for viscous flow calculation. (English) Zbl 0848.76071 Comput. Methods Appl. Mech. Eng. 118, No. 1-2, 47-61 (1994). MSC: 76M25 76D05 PDF BibTeX XML Cite \textit{H. H. Yang} and \textit{B. Shizgal}, Comput. Methods Appl. Mech. Eng. 118, No. 1--2, 47--61 (1994; Zbl 0848.76071) Full Text: DOI OpenURL
O’Sullivan, P. L.; Breuer, K. S. Transient growth in circular pipe flow. I: Linear disturbances. II: Nonlinear development. (English) Zbl 0848.76022 Phys. Fluids 6, No. 11, 3643-3664 (1994). Reviewer: Iuliana Oprea (Bucureşti) MSC: 76E05 76E30 76D05 PDF BibTeX XML Cite \textit{P. L. O'Sullivan} and \textit{K. S. Breuer}, Phys. Fluids 6, No. 11, 3643--3664 (1994; Zbl 0848.76022) Full Text: DOI OpenURL
Pécheux, J.; Le Quéré, P.; Abcha, F. Curvature effects on axisymmetric instability of conduction regime in a tall air-filled annulus. (English) Zbl 0825.76222 Phys. Fluids 6, No. 10, 3247-3255 (1994). MSC: 76E15 76R10 PDF BibTeX XML Cite \textit{J. Pécheux} et al., Phys. Fluids 6, No. 10, 3247--3255 (1994; Zbl 0825.76222) Full Text: DOI OpenURL
Zampieri, E. On the condition number of some spectral collocation operators and their finite element preconditioning. (English) Zbl 0822.65092 J. Sci. Comput. 9, No. 4, 419-443 (1994). Reviewer: W.Heinrichs (Düsseldorf) MSC: 65N35 65N30 65F35 65F10 35J25 PDF BibTeX XML Cite \textit{E. Zampieri}, J. Sci. Comput. 9, No. 4, 419--443 (1994; Zbl 0822.65092) Full Text: DOI OpenURL
Ma, Heping; Guo, Benyu The Chebyshev spectral method with a restraint operator for Burgers equation. (English) Zbl 0815.65117 Appl. Math., Ser. B (Engl. Ed.) 9, No. 3, 213-222 (1994). Reviewer: K.Najzar (Praha) MSC: 65N35 65N12 35Q53 PDF BibTeX XML Cite \textit{H. Ma} and \textit{B. Guo}, Appl. Math., Ser. B (Engl. Ed.) 9, No. 3, 213--222 (1994; Zbl 0815.65117) Full Text: DOI OpenURL
Graham, Michael D.; Steen, Paul H. Plume formation and resonant bifurcations in porous-media convection. (English) Zbl 0925.76735 J. Fluid Mech. 272, 67-89 (1994). MSC: 76S05 76R10 76E15 PDF BibTeX XML Cite \textit{M. D. Graham} and \textit{P. H. Steen}, J. Fluid Mech. 272, 67--89 (1994; Zbl 0925.76735) Full Text: DOI OpenURL
Xiong, Yue-Shan The errors estimation of the Chebyshev spectral-difference method for two-dimensional vorticity equation. (English) Zbl 0806.65120 Appl. Math., Ser. B (Engl. Ed.) 9, No. 2, 153-167 (1994). Reviewer: S.Jiang (Bonn) MSC: 65Z05 65M70 76M20 65M12 35Q35 76B47 PDF BibTeX XML Cite \textit{Y.-S. Xiong}, Appl. Math., Ser. B (Engl. Ed.) 9, No. 2, 153--167 (1994; Zbl 0806.65120) Full Text: DOI OpenURL
Najjar, F. M.; Vanka, S. P. Numerical study of a separated-reattaching flow. (English) Zbl 0794.76032 Theor. Comput. Fluid Dyn. 5, No. 6, 291-308 (1993). Reviewer: I.Teipel (Hannover) MSC: 76D10 76M20 PDF BibTeX XML Cite \textit{F. M. Najjar} and \textit{S. P. Vanka}, Theor. Comput. Fluid Dyn. 5, No. 6, 291--308 (1993; Zbl 0794.76032) Full Text: DOI OpenURL
Labrosse, G. Compatibility conditions for the Stokes system discretized in 2-D Cartesian domains. (English) Zbl 0783.76081 Comput. Methods Appl. Mech. Eng. 106, No. 3, 353-365 (1993). MSC: 76M99 76D07 PDF BibTeX XML Cite \textit{G. Labrosse}, Comput. Methods Appl. Mech. Eng. 106, No. 3, 353--365 (1993; Zbl 0783.76081) Full Text: DOI OpenURL
Yang, Henry H. The computational boundary method for solving the incompressible flows. (English) Zbl 0770.76052 Appl. Math. Lett. 6, No. 2, 3-7 (1993). MSC: 76M25 76D05 PDF BibTeX XML Cite \textit{H. H. Yang}, Appl. Math. Lett. 6, No. 2, 3--7 (1993; Zbl 0770.76052) Full Text: DOI OpenURL
Le Quéré, P. Accurate solutions to the square thermally driven cavity at high Rayleigh number. (English) Zbl 0731.76054 Comput. Fluids 20, No. 1, 29-41 (1991). MSC: 76M20 65N35 76R10 80A20 PDF BibTeX XML Cite \textit{P. Le Quéré}, Comput. Fluids 20, No. 1, 29--41 (1991; Zbl 0731.76054) Full Text: DOI OpenURL
Kapania, R. K.; Eldred, L. B. Solution of nonlinear partial differential equations using the Chebyshev spectral method. (English) Zbl 0739.73043 Comput. Mech. 8, No. 3, 173-179 (1991). Reviewer: B.D.Reddy (Rondebosch) MSC: 74S30 65N35 35Q72 PDF BibTeX XML Cite \textit{R. K. Kapania} and \textit{L. B. Eldred}, Comput. Mech. 8, No. 3, 173--179 (1991; Zbl 0739.73043) Full Text: DOI OpenURL
Chaouche, A.; Randriamampianina, A.; Bontoux, P. A collocation method based on the influence matrix technique for Navier- Stokes problems in annular domains. (English) Zbl 0722.76061 Comput. Methods Appl. Mech. Eng. 80, No. 1-3, 237-244 (1990). MSC: 76M25 76D05 PDF BibTeX XML Cite \textit{A. Chaouche} et al., Comput. Methods Appl. Mech. Eng. 80, No. 1--3, 237--244 (1990; Zbl 0722.76061) Full Text: DOI OpenURL
Le Quéré, P.; Pécheux, J. A three-dimensional pseudo-spectral algorithm for the computaion of convection in a rotating annulus. (English) Zbl 0722.76050 Comput. Methods Appl. Mech. Eng. 80, No. 1-3, 261-271 (1990). MSC: 76M25 76D05 76U05 PDF BibTeX XML Cite \textit{P. Le Quéré} and \textit{J. Pécheux}, Comput. Methods Appl. Mech. Eng. 80, No. 1--3, 261--271 (1990; Zbl 0722.76050) Full Text: DOI OpenURL
Le Quéré, P. Transition to unsteady natural convection in a tall water-filled cavity. (English) Zbl 0699.76093 Phys. Fluids, A 2, No. 4, 503-515 (1990). MSC: 76R10 76M99 PDF BibTeX XML Cite \textit{P. Le Quéré}, Phys. Fluids, A 2, No. 4, 503--515 (1990; Zbl 0699.76093) Full Text: DOI OpenURL
Heinrichs, Wilhelm Algebraic spectral multigrid methods. (English) Zbl 0742.65085 Comput. Methods Appl. Mech. Eng. 80, No. 1-3, 281-286 (1990). Reviewer: O.Widlund (New York) MSC: 65N55 65N35 65N06 35J05 PDF BibTeX XML Cite \textit{W. Heinrichs}, Comput. Methods Appl. Mech. Eng. 80, No. 1--3, 281--286 (1990; Zbl 0742.65085) Full Text: DOI OpenURL
Zampieri, E. Iterative methods for domain decomposition using spectral tau and collocation approximation. (English) Zbl 0692.65059 Calcolo 26, No. 1, 61-91 (1989). Reviewer: K.T.S.R.Iyengar MSC: 65N35 65F10 35J25 PDF BibTeX XML Cite \textit{E. Zampieri}, Calcolo 26, No. 1, 61--91 (1989; Zbl 0692.65059) Full Text: DOI OpenURL
Schultz, W. W.; Lee, N. Y.; Boyd, J. P. Chebyshev pseudospectral method of viscous flows with corner singularities. (English) Zbl 0679.76042 J. Sci. Comput. 4, No. 1, 1-24 (1989). MSC: 76D07 PDF BibTeX XML Cite \textit{W. W. Schultz} et al., J. Sci. Comput. 4, No. 1, 1--24 (1989; Zbl 0679.76042) Full Text: DOI OpenURL
Heinrichs, Wilhelm Improved condition number for spectral methods. (English) Zbl 0676.65115 Math. Comput. 53, No. 187, 103-119 (1989). Reviewer: H.R.Schwarz MSC: 65N35 65F35 35J05 35J25 PDF BibTeX XML Cite \textit{W. Heinrichs}, Math. Comput. 53, No. 187, 103--119 (1989; Zbl 0676.65115) Full Text: DOI OpenURL
Heinrichs, Wilhelm Spectral methods with sparse matrices. (English) Zbl 0661.65120 Numer. Math. 56, No. 1, 25-41 (1989). Reviewer: W.Heinrichs MSC: 65N35 65F10 35J05 PDF BibTeX XML Cite \textit{W. Heinrichs}, Numer. Math. 56, No. 1, 25--41 (1989; Zbl 0661.65120) Full Text: DOI EuDML OpenURL
Goldhirsch, Isaac; Pelz, Richard B.; Orszag, Steven A. Numerical simulation of thermal convection in a two-dimensional finite box. (English) Zbl 0659.76094 J. Fluid Mech. 199, 1-28 (1989). MSC: 76R05 76R10 76E15 76M99 PDF BibTeX XML Cite \textit{I. Goldhirsch} et al., J. Fluid Mech. 199, 1--28 (1989; Zbl 0659.76094) Full Text: DOI OpenURL
Farcy, A.; Alziary de Roquefort, T. Chebyshev pseudospectral solution of the incompressible Navier-Stokes equations in curvilinear domains. (English) Zbl 0669.76048 Comput. Fluids 16, No. 4, 459-473 (1988). MSC: 76D05 76M99 PDF BibTeX XML Cite \textit{A. Farcy} and \textit{T. Alziary de Roquefort}, Comput. Fluids 16, No. 4, 459--473 (1988; Zbl 0669.76048) Full Text: DOI OpenURL
Shen, Jie A spectral-Tau approximation for the Stokes and Navier-Stokes equations. (English) Zbl 0657.76031 RAIRO, Modélisation Math. Anal. Numér. 22, No. 4, 677-693 (1988). MSC: 76D05 76D07 65N35 PDF BibTeX XML Cite \textit{J. Shen}, RAIRO, Modélisation Math. Anal. Numér. 22, No. 4, 677--693 (1988; Zbl 0657.76031) Full Text: DOI EuDML OpenURL
Phillips, T. N.; Davies, A. R. On semi-infinite spectral elements for Poisson problems with re-entrant boundary singularities. (English) Zbl 0631.65104 J. Comput. Appl. Math. 21, No. 2, 173-188 (1988). Reviewer: P.-L.Lions MSC: 65N30 65N35 35J05 PDF BibTeX XML Cite \textit{T. N. Phillips} and \textit{A. R. Davies}, J. Comput. Appl. Math. 21, No. 2, 173--188 (1988; Zbl 0631.65104) Full Text: DOI OpenURL
Marcus, Philip S.; Tuckerman, Laurette S. Simulation of flow between concentric rotating spheres. I. Steady states. (English) Zbl 0645.76117 J. Fluid Mech. 185, 1-30 (1987). MSC: 76U05 76D10 76M99 PDF BibTeX XML Cite \textit{P. S. Marcus} and \textit{L. S. Tuckerman}, J. Fluid Mech. 185, 1--30 (1987; Zbl 0645.76117) Full Text: DOI OpenURL
Boyd, John P. An analytical and numerical study of the two-dimensional Bratu equation. (English) Zbl 0649.65057 J. Sci. Comput. 1, No. 2, 183-206 (1986). MSC: 65N25 65N35 35P30 PDF BibTeX XML Cite \textit{J. P. Boyd}, J. Sci. Comput. 1, No. 2, 183--206 (1986; Zbl 0649.65057) Full Text: DOI OpenURL
Sparis, Panagiotis D.; Mouroutsos, Spyridon G. The operational matrix of differentiation for orthogonal polynomial series. (English) Zbl 0595.44007 Int. J. Control 44, 1-15 (1986). MSC: 44A45 65L05 34A25 PDF BibTeX XML Cite \textit{P. D. Sparis} and \textit{S. G. Mouroutsos}, Int. J. Control 44, 1--15 (1986; Zbl 0595.44007) Full Text: DOI OpenURL
Marcus, Philip S. Simulation of Taylor-Couette flow. I. Numerical methods and comparison with experiment. (English) Zbl 0561.76037 J. Fluid Mech. 146, 45-64 (1984). MSC: 76D05 76M99 76-04 PDF BibTeX XML Cite \textit{P. S. Marcus}, J. Fluid Mech. 146, 45--64 (1984; Zbl 0561.76037) Full Text: DOI OpenURL
Haldenwang, P.; Labrosse, G.; Abboudi, S.; Deville, M. Chebyshev 3-D spectral and 2-D pseudospectral solvers for the Helmholtz equation. (English) Zbl 0544.65071 J. Comput. Phys. 55, 115-128 (1984). MSC: 65N25 65L15 34L99 35J05 35P15 PDF BibTeX XML Cite \textit{P. Haldenwang} et al., J. Comput. Phys. 55, 115--128 (1984; Zbl 0544.65071) Full Text: DOI OpenURL
Haidvogel, D. B.; Robinson, A. R.; Schulman, E. E. The accuracy, efficiency, and stability of three numerical models with application to open ocean problems. (English) Zbl 0495.76010 J. Comput. Phys. 34, 1-53 (1980). MSC: 76M99 76-02 86A05 76E20 PDF BibTeX XML Cite \textit{D. B. Haidvogel} et al., J. Comput. Phys. 34, 1--53 (1980; Zbl 0495.76010) Full Text: DOI OpenURL
Haidvogel, D. B.; Robinson, A. R.; Schulman, E. E. The accuracy, efficiency, and stability of three numerical models with application to open ocean problems. (English) Zbl 0489.76035 J. Comput. Phys. 34, 1-53 (1980). MSC: 76B65 76M99 86A05 76B47 PDF BibTeX XML Cite \textit{D. B. Haidvogel} et al., J. Comput. Phys. 34, 1--53 (1980; Zbl 0489.76035) Full Text: DOI OpenURL