Agocs, Fruzsina J.; Barnett, Alex H. An adaptive spectral method for oscillatory second-order linear ODEs with frequency-independent cost. (English) Zbl 07805451 SIAM J. Numer. Anal. 62, No. 1, 295-321 (2024). MSC: 65L60 34E05 PDFBibTeX XMLCite \textit{F. J. Agocs} and \textit{A. H. Barnett}, SIAM J. Numer. Anal. 62, No. 1, 295--321 (2024; Zbl 07805451) Full Text: DOI arXiv
Guo, Ruihan; Xu, Yan Semi-implicit spectral deferred correction methods based on second-order time integration schemes for nonlinear PDEs. (English) Zbl 07803024 J. Comput. Math. 42, No. 1, 111-133 (2024). MSC: 65M60 35L75 35G25 PDFBibTeX XMLCite \textit{R. Guo} and \textit{Y. Xu}, J. Comput. Math. 42, No. 1, 111--133 (2024; Zbl 07803024) Full Text: DOI
Shaidurov, Vladimir V.; Novikov, Anton E. Difference schemes for second-order ordinary differential equations with corrector and predictor properties. (English) Zbl 1496.65091 Russ. J. Numer. Anal. Math. Model. 37, No. 3, 175-187 (2022). MSC: 65L06 65L20 PDFBibTeX XMLCite \textit{V. V. Shaidurov} and \textit{A. E. Novikov}, Russ. J. Numer. Anal. Math. Model. 37, No. 3, 175--187 (2022; Zbl 1496.65091) Full Text: DOI
Nkoumbou Kaptchouang, Noé Brice; Gélébart, Lionel Multiscale coupling of FFT-based simulations with the LDC approach. (English) Zbl 1507.65279 Comput. Methods Appl. Mech. Eng. 394, Article ID 114921, 29 p. (2022). MSC: 65N55 PDFBibTeX XMLCite \textit{N. B. Nkoumbou Kaptchouang} and \textit{L. Gélébart}, Comput. Methods Appl. Mech. Eng. 394, Article ID 114921, 29 p. (2022; Zbl 1507.65279) Full Text: DOI
Maia, A. A. G.; Cavalca, D. F.; Tomita, J. T.; Costa, F. P.; Bringhenti, C. Evaluation of an effective and robust implicit time-integration numerical scheme for Navier-Stokes equations in a CFD solver for compressible flows. (English) Zbl 1510.76113 Appl. Math. Comput. 413, Article ID 126612, 15 p. (2022). MSC: 76M20 65M08 PDFBibTeX XMLCite \textit{A. A. G. Maia} et al., Appl. Math. Comput. 413, Article ID 126612, 15 p. (2022; Zbl 1510.76113) Full Text: DOI
Sun, Chong; Xia, Yinhua Asymptotic preserving spectral deferred correction methods for hyperbolic systems with relaxation. (English) Zbl 1473.65244 Commun. Comput. Phys. 26, No. 2, 531-557 (2019). MSC: 65M70 65B05 35L45 PDFBibTeX XMLCite \textit{C. Sun} and \textit{Y. Xia}, Commun. Comput. Phys. 26, No. 2, 531--557 (2019; Zbl 1473.65244) Full Text: DOI
Ceniceros, Hector D. Efficient order-adaptive methods for polymer self-consistent field theory. (English) Zbl 1452.82030 J. Comput. Phys. 386, 9-21 (2019). MSC: 82D60 65N50 82M22 PDFBibTeX XMLCite \textit{H. D. Ceniceros}, J. Comput. Phys. 386, 9--21 (2019; Zbl 1452.82030) Full Text: DOI
Hashemi, Behnam Enclosing Chebyshev expansions in linear time. (English) Zbl 1486.65047 ACM Trans. Math. Softw. 45, No. 3, Article No. 27, 33 p. (2019). MSC: 65G20 65D99 65G50 68Q25 PDFBibTeX XMLCite \textit{B. Hashemi}, ACM Trans. Math. Softw. 45, No. 3, Article No. 27, 33 p. (2019; Zbl 1486.65047) Full Text: DOI
Greengard, Leslie; Jiang, Shidong A new mixed potential representation for unsteady, incompressible flow. (English) Zbl 1429.35055 SIAM Rev. 61, No. 4, 733-755 (2019). MSC: 35J05 35J08 35K05 35K08 35Q30 PDFBibTeX XMLCite \textit{L. Greengard} and \textit{S. Jiang}, SIAM Rev. 61, No. 4, 733--755 (2019; Zbl 1429.35055) Full Text: DOI arXiv
Zhang, Bo; Chen, Dangxing; Huang, Jingfang On the Gauss Runge-Kutta and method of lines transpose for initial-boundary value parabolic PDEs. (English) Zbl 1475.65100 Commun. Comput. Phys. 24, No. 4, 1221-1240 (2018). MSC: 65M20 65L06 65M22 65M12 65M70 PDFBibTeX XMLCite \textit{B. Zhang} et al., Commun. Comput. Phys. 24, No. 4, 1221--1240 (2018; Zbl 1475.65100) Full Text: DOI
Boscarino, Sebastiano; Qiu, Jing-Mei; Russo, Giovanni Implicit-explicit integral deferred correction methods for stiff problems. (English) Zbl 1453.65153 SIAM J. Sci. Comput. 40, No. 2, A787-A816 (2018). MSC: 65L04 65L06 65L80 PDFBibTeX XMLCite \textit{S. Boscarino} et al., SIAM J. Sci. Comput. 40, No. 2, A787--A816 (2018; Zbl 1453.65153) Full Text: DOI arXiv
Römer, Ulrich; Schöps, Sebastian; De Gersem, Herbert A defect corrected finite element approach for the accurate evaluation of magnetic fields on unstructured grids. (English) Zbl 1375.78009 J. Comput. Phys. 335, 688-699 (2017). MSC: 78A30 78M10 PDFBibTeX XMLCite \textit{U. Römer} et al., J. Comput. Phys. 335, 688--699 (2017; Zbl 1375.78009) Full Text: DOI arXiv
Liu, Jun; Jiang, Yao-Lin; Wang, Yan A fast and stable algorithm for linear parabolic partial differential equations. (English) Zbl 1375.65138 Numer. Algorithms 75, No. 3, 699-729 (2017). MSC: 65M70 35K20 65M12 PDFBibTeX XMLCite \textit{J. Liu} et al., Numer. Algorithms 75, No. 3, 699--729 (2017; Zbl 1375.65138) Full Text: DOI
Liu, Jun; Wang, Yan; Li, Rongjian A hybrid algorithm based on optimal quadratic spline collocation and parareal deferred correction for parabolic PDEs. (English) Zbl 1400.65054 Math. Probl. Eng. 2016, Article ID 6943079, 15 p. (2016). MSC: 65M70 65L05 65Y05 PDFBibTeX XMLCite \textit{J. Liu} et al., Math. Probl. Eng. 2016, Article ID 6943079, 15 p. (2016; Zbl 1400.65054) Full Text: DOI
Amore, Paolo; Boyd, John P.; Fernández, Francisco M.; Rösler, Boris High order eigenvalues for the Helmholtz equation in complicated non-tensor domains through Richardson extrapolation of second order finite differences. (English) Zbl 1352.65458 J. Comput. Phys. 312, 252-271 (2016). MSC: 65N25 65N06 PDFBibTeX XMLCite \textit{P. Amore} et al., J. Comput. Phys. 312, 252--271 (2016; Zbl 1352.65458) Full Text: DOI arXiv
Quaife, Bryan; Biros, George Adaptive time stepping for vesicle suspensions. (English) Zbl 1351.76325 J. Comput. Phys. 306, 478-499 (2016). MSC: 76Z05 65L60 92C35 PDFBibTeX XMLCite \textit{B. Quaife} and \textit{G. Biros}, J. Comput. Phys. 306, 478--499 (2016; Zbl 1351.76325) Full Text: DOI arXiv
Boscarino, Sebastiano; Qiu, Jing-Mei Error estimates of the integral deferred correction method for stiff problems. (English) Zbl 1364.65151 ESAIM, Math. Model. Numer. Anal. 50, No. 4, 1137-1166 (2016). Reviewer: Michael Plum (Karlsruhe) MSC: 65L20 65-XX 65L05 65L04 65B05 65L11 65L06 PDFBibTeX XMLCite \textit{S. Boscarino} and \textit{J.-M. Qiu}, ESAIM, Math. Model. Numer. Anal. 50, No. 4, 1137--1166 (2016; Zbl 1364.65151) Full Text: DOI arXiv
Napoli, Anna Solutions of linear second order initial value problems by using Bernoulli polynomials. (English) Zbl 1329.65146 Appl. Numer. Math. 99, 109-120 (2016). MSC: 65L05 65L06 PDFBibTeX XMLCite \textit{A. Napoli}, Appl. Numer. Math. 99, 109--120 (2016; Zbl 1329.65146) Full Text: DOI
Christlieb, Andrew J.; Liu, Yuan; Xu, Zhengfu High order operator splitting methods based on an integral deferred correction framework. (English) Zbl 1349.65210 J. Comput. Phys. 294, 224-242 (2015). MSC: 65L05 65M20 PDFBibTeX XMLCite \textit{A. J. Christlieb} et al., J. Comput. Phys. 294, 224--242 (2015; Zbl 1349.65210) Full Text: DOI arXiv
Haynes, Ronald D.; Ong, Benjamin W. MPI-OpenMP algorithms for the parallel space-time solution of time dependent PDEs. (English) Zbl 1382.65243 Erhel, Jocelyne (ed.) et al., Domain decomposition methods in science and engineering XXI. Proceedings of the 21st international conference, Inria Rennes Center, France, June 25–29, 2012. Cham: Springer (ISBN 978-3-319-05788-0/hbk; 978-3-319-35548-1/pbk; 978-3-319-05789-7/ebook). Lecture Notes in Computational Science and Engineering 98, 179-187 (2014). MSC: 65M06 34K05 65M55 65Y05 PDFBibTeX XMLCite \textit{R. D. Haynes} and \textit{B. W. Ong}, Lect. Notes Comput. Sci. Eng. 98, 179--187 (2014; Zbl 1382.65243) Full Text: DOI
Musa, H.; Suleiman, M. B.; Ismail, F.; Senu, N.; Ibrahim, Z. B. An accurate block solver for stiff initial value problems. (English) Zbl 1298.65048 ISRN Appl. Math. 2013, Article ID 567451, 10 p. (2013). MSC: 65F05 35M99 PDFBibTeX XMLCite \textit{H. Musa} et al., ISRN Appl. Math. 2013, Article ID 567451, 10 p. (2013; Zbl 1298.65048) Full Text: DOI
Zhang, Yunzhang; Hou, Yanren; Yang, Ganshan A defect-correction method for time-dependent viscoelastic fluid flow based on SUPG formulation. (English) Zbl 1284.76260 Discrete Dyn. Nat. Soc. 2011, Article ID 689804, 25 p. (2011). MSC: 76M10 65M60 76A10 PDFBibTeX XMLCite \textit{Y. Zhang} et al., Discrete Dyn. Nat. Soc. 2011, Article ID 689804, 25 p. (2011; Zbl 1284.76260) Full Text: DOI
Shishkin, G. I.; Shishkina, L. P. A Richardson scheme of an increased order of accuracy for a semilinear singularly perturbed elliptic convection-diffusion equation. (Russian. English summary) Zbl 07818370 Zh. Vychisl. Mat. Mat. Fiz. 50, No. 3, 458-478 (2010); translation in Comput. Math. Math. Phys. 50, No. 3, 437-456 (2010). MSC: 65N12 PDFBibTeX XMLCite \textit{G. I. Shishkin} and \textit{L. P. Shishkina}, Zh. Vychisl. Mat. Mat. Fiz. 50, No. 3, 458--478 (2010; Zbl 07818370); translation in Comput. Math. Math. Phys. 50, No. 3, 437--456 (2010) Full Text: DOI MNR
Ervin, Vincent J.; Howell, Jason S.; Lee, Hyesuk A two-parameter defect-correction method for computation of steady-state viscoelastic fluid flow. (English) Zbl 1132.76033 Appl. Math. Comput. 196, No. 2, 818-834 (2008). MSC: 76M10 76A10 PDFBibTeX XMLCite \textit{V. J. Ervin} et al., Appl. Math. Comput. 196, No. 2, 818--834 (2008; Zbl 1132.76033) Full Text: DOI
Huang, Jingfang; Jia, Jun; Minion, Michael Accelerating the convergence of spectral deferred correction methods. (English) Zbl 1094.65066 J. Comput. Phys. 214, No. 2, 633-656 (2006). Reviewer: Manuel Calvo (Zaragoza) MSC: 65L05 34A30 34A34 65F10 65F35 65L60 PDFBibTeX XMLCite \textit{J. Huang} et al., J. Comput. Phys. 214, No. 2, 633--656 (2006; Zbl 1094.65066) Full Text: DOI
Wang, Z. K.; Djambazov, G. S.; Lai, C.-H.; Pericleous, K. A. An acoustic correction method for extracting sound signals. (English) Zbl 1068.76076 Comput. Math. Appl. 47, No. 1, 57-69 (2004). MSC: 76Q05 76M25 PDFBibTeX XMLCite \textit{Z. K. Wang} et al., Comput. Math. Appl. 47, No. 1, 57--69 (2004; Zbl 1068.76076) Full Text: DOI
Djambazov, G. S.; Lai, C.-H.; Pericleous, K. A.; Wang, Z.-K. A coarse grid extraction of sound signals for computational aeroacoustics. (English) Zbl 1025.76026 Int. J. Numer. Methods Fluids 40, No. 12, 1515-1525 (2002). MSC: 76M20 76Q05 PDFBibTeX XMLCite \textit{G. S. Djambazov} et al., Int. J. Numer. Methods Fluids 40, No. 12, 1515--1525 (2002; Zbl 1025.76026) Full Text: DOI
Chibi, Ahmed-Salah Defect correction and domain decomposition for second-order boundary value problems. (English) Zbl 1012.65133 J. Comput. Appl. Math. 130, No. 1-2, 41-51 (2001). MSC: 65N55 65N15 65N30 35J25 PDFBibTeX XMLCite \textit{A.-S. Chibi}, J. Comput. Appl. Math. 130, No. 1--2, 41--51 (2001; Zbl 1012.65133) Full Text: DOI
Butcher, J. C.; Cash, J. R.; Moore, G.; Russell, R. D. Defect correction for two-point boundary value problems on nonequidistant meshes. (English) Zbl 0828.65102 Math. Comput. 64, No. 210, 629-648 (1995). Reviewer: P.Chocholatý (Bratislava) MSC: 65L10 65L12 65L50 34B15 PDFBibTeX XMLCite \textit{J. C. Butcher} et al., Math. Comput. 64, No. 210, 629--648 (1995; Zbl 0828.65102) Full Text: DOI
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Moore, Gerald Defect correction from a Galerkin viewpoint. (English) Zbl 0643.65051 Numer. Math. 52, No. 5, 565-582 (1988). Reviewer: I.N.Katz MSC: 65L10 65L60 34B15 PDFBibTeX XMLCite \textit{G. Moore}, Numer. Math. 52, No. 5, 565--582 (1988; Zbl 0643.65051) Full Text: DOI EuDML
Böhmer, K.; Römer, Thomas Grid strategy and high accuracy via defect corrections for the Kreiss- method for stiff boundary value problems. (English) Zbl 0615.65086 Computing 38, 269-273 (1987). MSC: 65L10 65L50 34B05 PDFBibTeX XMLCite \textit{K. Böhmer} and \textit{T. Römer}, Computing 38, 269--273 (1987; Zbl 0615.65086) Full Text: DOI