Dhaouadi, Firas; Dumbser, Michael A first order hyperbolic reformulation of the Navier-Stokes-Korteweg system based on the GPR model and an augmented Lagrangian approach. (English) Zbl 07599597 J. Comput. Phys. 470, Article ID 111544, 30 p. (2022). MSC: 65Mxx 76Mxx 35Lxx PDFBibTeX XMLCite \textit{F. Dhaouadi} and \textit{M. Dumbser}, J. Comput. Phys. 470, Article ID 111544, 30 p. (2022; Zbl 07599597) Full Text: DOI
Andò, Alessia; Breda, Dimitri Convergence analysis of collocation methods for computing periodic solutions of retarded functional differential equations. (English) Zbl 1487.65081 SIAM J. Numer. Anal. 58, No. 5, 3010-3039 (2020). Reviewer: Raffaella Pavani (Milano) MSC: 65L03 34K10 34K13 65L10 65L20 65L60 PDFBibTeX XMLCite \textit{A. Andò} and \textit{D. Breda}, SIAM J. Numer. Anal. 58, No. 5, 3010--3039 (2020; Zbl 1487.65081) Full Text: DOI arXiv
Yuan, Si; Dong, Yiyi; Xing, Qinyan; Fang, Nan Adaptive finite element method of lines with local mesh refinement in maximum norm based on element energy projection method. (English) Zbl 1476.65313 Int. J. Comput. Methods 17, No. 4, Article ID 1950008, 18 p. (2020). MSC: 65N30 65N50 PDFBibTeX XMLCite \textit{S. Yuan} et al., Int. J. Comput. Methods 17, No. 4, Article ID 1950008, 18 p. (2020; Zbl 1476.65313) Full Text: DOI
Burkotová, Jana; Rachunková, Irena; Weinmüller, Ewa B. On singular BVPs with nonsmooth data: convergence of the collocation schemes. (English) Zbl 1421.65021 BIT 57, No. 4, 1153-1184 (2017). Reviewer: Fernando Casas (Castellon) MSC: 65L60 65L20 65L05 65L10 PDFBibTeX XMLCite \textit{J. Burkotová} et al., BIT 57, No. 4, 1153--1184 (2017; Zbl 1421.65021) Full Text: DOI
Khuri, S. A.; Sayfy, A. A mixed decomposition-spline approach for the numerical solution of a class of singular boundary value problems. (English) Zbl 1459.65115 Appl. Math. Modelling 40, No. 7-8, 4664-4680 (2016). MSC: 65L10 65L20 65L60 PDFBibTeX XMLCite \textit{S. A. Khuri} and \textit{A. Sayfy}, Appl. Math. Modelling 40, No. 7--8, 4664--4680 (2016; Zbl 1459.65115) Full Text: DOI
Kuehn, Christian Efficient gluing of numerical continuation and a multiple solution method for elliptic PDEs. (English) Zbl 1410.65480 Appl. Math. Comput. 266, 656-674 (2015). MSC: 65P30 65N30 35B32 35J25 35J61 PDFBibTeX XMLCite \textit{C. Kuehn}, Appl. Math. Comput. 266, 656--674 (2015; Zbl 1410.65480) Full Text: DOI arXiv
Lamour, René; März, Roswitha; Weinmüller, Ewa Boundary-value problems for differential-algebraic equations: A survey. (English) Zbl 1343.65102 Ilchmann, Achim (ed.) et al., Surveys in differential-algebraic equations III. Cham: Springer (ISBN 978-3-319-22427-5/pbk; 978-3-319-22428-2/ebook). Differential-Algebraic Equations Forum, 177-309 (2015). Reviewer: Boris V. Loginov (Ul’yanovsk) MSC: 65L80 34A09 34B05 34B15 65L60 65L70 65L12 PDFBibTeX XMLCite \textit{R. Lamour} et al., in: Surveys in differential-algebraic equations III. Cham: Springer. 177--309 (2015; Zbl 1343.65102) Full Text: DOI
De Witte, V.; Govaerts, W. Convergence analysis of a numerical method to solve the adjoint linearized periodic orbit equations. (English) Zbl 1206.65195 Appl. Numer. Math. 60, No. 10, 1007-1023 (2010). Reviewer: Raffaella Pavani (Milano) MSC: 65L20 65L60 65L05 34C05 34C25 37C27 PDFBibTeX XMLCite \textit{V. De Witte} and \textit{W. Govaerts}, Appl. Numer. Math. 60, No. 10, 1007--1023 (2010; Zbl 1206.65195) Full Text: DOI Link
Cash, J.; Kitzhofer, G.; Koch, O.; Moore, G.; Weinmüller, E. Numerical solution of singular two point BVPs. (English) Zbl 1191.65099 JNAIAM, J. Numer. Anal. Ind. Appl. Math. 4, No. 1-2, 129-149 (2009). MSC: 65L10 65L60 34B16 65Y20 PDFBibTeX XMLCite \textit{J. Cash} et al., JNAIAM, J. Numer. Anal. Ind. Appl. Math. 4, No. 1--2, 129--149 (2009; Zbl 1191.65099)
Yuan, Si; Xing, Qin-Yan; Wang, Xu; Ye, Kang-Sheng Self-adaptive strategy for one-dimensional finite element method based on EEP method with optimal super-convergence order. (English) Zbl 1231.65122 Appl. Math. Mech., Engl. Ed. 29, No. 5, 591-602 (2008). MSC: 65L10 65L50 65L60 PDFBibTeX XMLCite \textit{S. Yuan} et al., Appl. Math. Mech., Engl. Ed. 29, No. 5, 591--602 (2008; Zbl 1231.65122) Full Text: DOI
Finden, W. F. Higher order approximations using interpolation applied to collocation solutions of two-point boundary value problems. (English) Zbl 1131.65063 J. Comput. Appl. Math. 206, No. 1, 99-115 (2007). Reviewer: Johannes Schropp (Konstanz) MSC: 65L10 65L60 65L70 34B05 PDFBibTeX XMLCite \textit{W. F. Finden}, J. Comput. Appl. Math. 206, No. 1, 99--115 (2007; Zbl 1131.65063) Full Text: DOI
Wright, K. Adaptive methods for piecewise polynomial collocation for ordinary differential equations. (English) Zbl 1116.65095 BIT 47, No. 1, 197-212 (2007). MSC: 65L10 65L60 34B05 65L70 PDFBibTeX XMLCite \textit{K. Wright}, BIT 47, No. 1, 197--212 (2007; Zbl 1116.65095) Full Text: DOI
Yuan, Si; He, Xue-Feng Self-adaptive strategy for one-dimensional finite element method based on element energy projection method. (English) Zbl 1231.65121 Appl. Math. Mech., Engl. Ed. 27, No. 11, 1461-1474 (2006). MSC: 65L10 65L50 65L60 PDFBibTeX XMLCite \textit{S. Yuan} and \textit{X.-F. He}, Appl. Math. Mech., Engl. Ed. 27, No. 11, 1461--1474 (2006; Zbl 1231.65121) Full Text: DOI
Auzinger, Winfried; Karner, Ernst; Koch, Othmar; Weinmüller, Ewa Collocation methods for the solution of eigenvalue problems for singular ordinary differential equations. (English) Zbl 1132.65070 Opusc. Math. 26, No. 2, 229-241 (2006). MSC: 65L15 34L16 34L30 65L60 65L70 65L50 PDFBibTeX XMLCite \textit{W. Auzinger} et al., Opusc. Math. 26, No. 2, 229--241 (2006; Zbl 1132.65070)
Ramachandran, P. A. Boundary integral method for multispecies 1-D convection-diffusion-reaction problems. (English) Zbl 1075.65103 Comput. Math. Appl. 49, No. 9-10, 1575-1583 (2005). MSC: 65L10 65L60 80M15 34B15 80A32 PDFBibTeX XMLCite \textit{P. A. Ramachandran}, Comput. Math. Appl. 49, No. 9--10, 1575--1583 (2005; Zbl 1075.65103) Full Text: DOI
Ganesh, M.; Grigorieff, R. D.; Mustapha, K. Discrete Petrov-Galerkin scheme for boundary value differential and integral problems: Theory and applications. (English) Zbl 1075.65105 Math. Comput. Modelling 40, No. 11-12, 1323-1334 (2004). Reviewer: Emil Minchev (Tokyo) MSC: 65L60 65R20 34B15 65L10 45J05 34E15 45G10 PDFBibTeX XMLCite \textit{M. Ganesh} et al., Math. Comput. Modelling 40, No. 11--12, 1323--1334 (2004; Zbl 1075.65105) Full Text: DOI
Tasci, Fatih On the approximative solution of boundary value problems by collocation. (English) Zbl 1047.65062 Far East J. Appl. Math. 12, No. 1, 11-20 (2003). MSC: 65L60 65L10 34B15 PDFBibTeX XMLCite \textit{F. Tasci}, Far East J. Appl. Math. 12, No. 1, 11--20 (2003; Zbl 1047.65062)
Luzyanina, Tatyana; Engelborghs, Koen Computing Floquet multipliers for functional differential equations. (English) Zbl 1048.65126 Int. J. Bifurcation Chaos Appl. Sci. Eng. 12, No. 12, 2977-2989 (2002). MSC: 65P30 37M20 37G15 65L60 34K13 34K28 34K20 34K18 PDFBibTeX XMLCite \textit{T. Luzyanina} and \textit{K. Engelborghs}, Int. J. Bifurcation Chaos Appl. Sci. Eng. 12, No. 12, 2977--2989 (2002; Zbl 1048.65126) Full Text: DOI
Auzinger, Winfried; Koch, Othmar; Weinmüller, Ewa Efficient collocation schemes for singular boundary value problems. (English) Zbl 1021.65038 Numer. Algorithms 31, No. 1-4, 5-25 (2002). Reviewer: Laura-Iulia Aniţa (Iaşi) MSC: 65L10 34B16 65L60 65L50 65L70 PDFBibTeX XMLCite \textit{W. Auzinger} et al., Numer. Algorithms 31, No. 1--4, 5--25 (2002; Zbl 1021.65038) Full Text: DOI
Engelborghs, K.; Doedel, E. J. Stability of piecewise polynomial collocation for computing periodic solutions of delay differential equations. (English) Zbl 1002.65089 Numer. Math. 91, No. 4, 627-648 (2002). Reviewer: Laura-Iulia Aniţa (Iaşi) MSC: 65L60 65L20 65L50 34K28 34K13 PDFBibTeX XMLCite \textit{K. Engelborghs} and \textit{E. J. Doedel}, Numer. Math. 91, No. 4, 627--648 (2002; Zbl 1002.65089) Full Text: DOI
Sun, W.; Liu, K. M. Iterative algorithms for nonlinear ordinary differential eigenvalue problems. (English) Zbl 0988.65056 Appl. Numer. Math. 38, No. 3, 361-376 (2001). Reviewer: Nikolai L.Vulchanov (Warszawa) MSC: 65L15 65L20 65L12 65L60 34L30 34L16 PDFBibTeX XMLCite \textit{W. Sun} and \textit{K. M. Liu}, Appl. Numer. Math. 38, No. 3, 361--376 (2001; Zbl 0988.65056) Full Text: DOI
Marušić, Miljenko A fourth/second order accurate collocation method for singularly perturbed two-point boundary value problems using tension splines. (English) Zbl 0989.65082 Numer. Math. 88, No. 1, 135-158 (2001). Reviewer: Walter Schempp (Siegen) MSC: 65L60 65L10 65L20 65L70 34B15 34E15 PDFBibTeX XMLCite \textit{M. Marušić}, Numer. Math. 88, No. 1, 135--158 (2001; Zbl 0989.65082) Full Text: DOI
Gremaud, Pierre A.; Matthews, John V. On the computation of steady hopper flows. I: Stress determination for Coulomb materials. (English) Zbl 1013.74015 J. Comput. Phys. 166, No. 1, 63-83 (2001). MSC: 74E20 74S30 74S20 76T25 PDFBibTeX XMLCite \textit{P. A. Gremaud} and \textit{J. V. Matthews}, J. Comput. Phys. 166, No. 1, 63--83 (2001; Zbl 1013.74015) Full Text: DOI
Amodio, P.; Cash, J. R.; Roussos, G.; Wright, R. W.; Fairweather, G.; Gladwell, I.; Kraut, G. L.; Paprzycki, M. Almost block diagonal linear systems: sequential and parallel solution techniques, and applications. (English) Zbl 1051.65018 Numer. Linear Algebra Appl. 7, No. 5, 275-317 (2000). Reviewer: Jan Chleboun (Praha) MSC: 65F05 65F10 65Y05 65L10 65-02 65L12 65L60 34B05 PDFBibTeX XMLCite \textit{P. Amodio} et al., Numer. Linear Algebra Appl. 7, No. 5, 275--317 (2000; Zbl 1051.65018) Full Text: DOI
Adomaitis, Raymond A.; Lin, Yi-hung; Chang, Hsiao-Yung A computational framework for boundary-value problem based simulations. (English) Zbl 1038.68594 Simulation 74, No. 1, 28-38 (2000). MSC: 68U20 PDFBibTeX XML Full Text: DOI Link
Sun, Weiwei Spectral analysis of Hermite cubic spline collocation systems. (English) Zbl 0937.65110 SIAM J. Numer. Anal. 36, No. 6, 1962-1975 (1999). Reviewer: Thomas Sonar (Braunschweig) MSC: 65M70 65N35 65L60 65L10 34B05 35K15 PDFBibTeX XMLCite \textit{W. Sun}, SIAM J. Numer. Anal. 36, No. 6, 1962--1975 (1999; Zbl 0937.65110) Full Text: DOI
Doedel, Eusebius On the construction of discretizations of elliptic partial differential equations. (English) Zbl 0907.65117 J. Difference Equ. Appl. 3, No. 5-6, 389-416 (1998). Reviewer: P.Chocholatý (Bratislava) MSC: 65N35 65N30 35J25 35J65 65N06 PDFBibTeX XMLCite \textit{E. Doedel}, J. Difference Equ. Appl. 3, No. 5--6, 389--416 (1998; Zbl 0907.65117) Full Text: DOI
Ahmed, A. H. Improved implementations of adaptive algorithms in collocation for boundary value problems. (English) Zbl 0892.65052 Int. J. Comput. Math. 66, No. 3-4, 267-275 (1998). Reviewer: P.Chocholatý (Bratislava) MSC: 65L10 65L60 34B15 PDFBibTeX XMLCite \textit{A. H. Ahmed}, Int. J. Comput. Math. 66, No. 3--4, 267--275 (1998; Zbl 0892.65052) Full Text: DOI
Wright, R.; Cash, J.; Moore, G. Mesh selection for stiff two-point boundary value problems. (English) Zbl 0804.65077 Numer. Algorithms 7, No. 2-4, 205-224 (1994). Reviewer: P.Chocholatý (Bratislava) MSC: 65L10 65L60 65L50 34E13 34B05 PDFBibTeX XMLCite \textit{R. Wright} et al., Numer. Algorithms 7, No. 2--4, 205--224 (1994; Zbl 0804.65077) Full Text: DOI
Ascher, Uri M.; Spiteri, Raymond J. Collocation software for boundary value differential-algebraic equations. (English) Zbl 0804.65080 SIAM J. Sci. Comput. 15, No. 4, 938-952 (1994). Reviewer: P.Chocholatý (Bratislava) MSC: 65L10 65L60 34-04 34B15 PDFBibTeX XMLCite \textit{U. M. Ascher} and \textit{R. J. Spiteri}, SIAM J. Sci. Comput. 15, No. 4, 938--952 (1994; Zbl 0804.65080) Full Text: DOI Link
Sloan, Ian H.; Tran, Dat; Fairweather, Graeme A fourth-order cubic spline method for linear second-order two-point boundary-value problems. (English) Zbl 0790.65078 IMA J. Numer. Anal. 13, No. 4, 591-607 (1993). Reviewer: M.M.Konstantinov (Sofia) MSC: 65L10 65L60 34B05 PDFBibTeX XMLCite \textit{I. H. Sloan} et al., IMA J. Numer. Anal. 13, No. 4, 591--607 (1993; Zbl 0790.65078) Full Text: DOI
Ascher, Uri M.; Petzold, Linda R. Projected collocation for higher-order higher-index differential- algebraic equations. (English) Zbl 0772.65049 J. Comput. Appl. Math. 43, No. 1-2, 243-259 (1992). Reviewer: M.M.Konstantinov (Sofia) MSC: 65L10 65L20 65L60 34A30 PDFBibTeX XMLCite \textit{U. M. Ascher} and \textit{L. R. Petzold}, J. Comput. Appl. Math. 43, No. 1--2, 243--259 (1992; Zbl 0772.65049) Full Text: DOI
Cash, J. R.; Wright, M. H. A deferred correction method for nonlinear two-point boundary value problems: Implementation and numerical evaluation. (English) Zbl 0727.65070 SIAM J. Sci. Stat. Comput. 12, No. 4, 971-989 (1991). Reviewer: E.Pfeifer (Dresden) MSC: 65L10 65L60 65L50 65L06 34B15 34E15 PDFBibTeX XMLCite \textit{J. R. Cash} and \textit{M. H. Wright}, SIAM J. Sci. Stat. Comput. 12, No. 4, 971--989 (1991; Zbl 0727.65070) Full Text: DOI
Mills, P. L.; Ramachandran, P. A. Mathematical modelling of chemical engineering systems by finite element analysis using PDE/PROTRAN. (English) Zbl 0701.65087 Comput. Math. Appl. 15, No. 9, 769-794 (1988). Reviewer: J.Appeltauer MSC: 65Z05 65N30 35-04 80A32 35Q35 PDFBibTeX XMLCite \textit{P. L. Mills} and \textit{P. A. Ramachandran}, Comput. Math. Appl. 15, No. 9, 769--794 (1988; Zbl 0701.65087) Full Text: DOI
Karageorghis, Andreas Chebyshev spectral methods for solving two-point boundary value problems arising in heat transfer. (English) Zbl 0636.65083 Comput. Methods Appl. Mech. Eng. 70, No. 1, 103-121 (1988). Reviewer: A.Karageorghis MSC: 65L10 34B15 34L99 65L60 PDFBibTeX XMLCite \textit{A. Karageorghis}, Comput. Methods Appl. Mech. Eng. 70, No. 1, 103--121 (1988; Zbl 0636.65083) Full Text: DOI
Greenwell-Yanik, C. E.; Fairweather, G. Analyses of spline collocation methods for parabolic and hyperbolic problems in two space variables. (English) Zbl 0595.65122 SIAM J. Numer. Anal. 23, 282-296 (1986). Reviewer: Michael Sever (Jerusalem) MSC: 65N35 65N30 65N15 35K60 PDFBibTeX XMLCite \textit{C. E. Greenwell-Yanik} and \textit{G. Fairweather}, SIAM J. Numer. Anal. 23, 282--296 (1986; Zbl 0595.65122) Full Text: DOI
Coyle, J. Michael; Flaherty, Joseph E.; Ludwig, Raymond On the stability of mesh equidistribution strategies for time-dependent partial differential equations. (English) Zbl 0579.65122 J. Comput. Phys. 62, 26-39 (1986). Reviewer: A.Hedstrom MSC: 65N50 65N12 65N30 PDFBibTeX XMLCite \textit{J. M. Coyle} et al., J. Comput. Phys. 62, 26--39 (1986; Zbl 0579.65122) Full Text: DOI
Sleptsov, A. G. The spline-collocation and the spline-Galerkin methods for Orr-Sommerfeld problem. (English) Zbl 0587.76060 Numerical boundary value ODEs, Proc. Int. Workshop, Vancouver/Can. 1984, Prog. Sci. Comput. 5, 137-147 (1985). MSC: 76E05 65L10 76M99 65D07 PDFBibTeX XML
Ascher, U.; Pruess, S.; Russell, R. D. On spline basis selection for solving differential equations. (English) Zbl 0525.65060 SIAM J. Numer. Anal. 20, 121-142 (1983). MSC: 65L10 65L60 65L50 PDFBibTeX XMLCite \textit{U. Ascher} et al., SIAM J. Numer. Anal. 20, 121--142 (1983; Zbl 0525.65060) Full Text: DOI
Russell, Robert D. Global codes for BVODEs and their comparison. (English) Zbl 0503.65056 Numerical integration of differential equations and large linear systems, Proc. Workshops, Bielefeld 1980, Lect. Notes Math. 968, 256-268 (1982). MSC: 65L10 65L60 34B15 PDFBibTeX XML
Davis, Stephen F.; Flaherty, Joseph E. An adaptive finite element method for initial-boundary value problems for partial differential equations. (English) Zbl 0478.65063 SIAM J. Sci. Stat. Comput. 3, 6-27 (1982). MSC: 65N30 65N15 35K60 PDFBibTeX XMLCite \textit{S. F. Davis} and \textit{J. E. Flaherty}, SIAM J. Sci. Stat. Comput. 3, 6--27 (1982; Zbl 0478.65063) Full Text: DOI