Skelton, Andrew; Willms, Allan R. Parameter range reduction from partial data in systems of differential algebraic equations. (English) Zbl 1441.93056 J. Comput. Appl. Math. 372, Article ID 112698, 12 p. (2020). Reviewer: Hannemann-Tamás (Aachen) MSC: 93B30 34A09 34A55 65G40 65L80 PDFBibTeX XMLCite \textit{A. Skelton} and \textit{A. R. Willms}, J. Comput. Appl. Math. 372, Article ID 112698, 12 p. (2020; Zbl 1441.93056) Full Text: DOI
Pryce, John D.; Nedialkov, Nedialko S.; Tan, Guangning; Li, Xiao How AD can help solve differential-algebraic equations. (English) Zbl 1409.65050 Optim. Methods Softw. 33, No. 4-6, 729-749 (2018). Reviewer: Phi Ha (Hanoi) MSC: 65L80 34A09 68W30 PDFBibTeX XMLCite \textit{J. D. Pryce} et al., Optim. Methods Softw. 33, No. 4--6, 729--749 (2018; Zbl 1409.65050) Full Text: DOI arXiv Link
Al Sakkaf, Laila Y.; Al-Mdallal, Qasem M.; Al Khawaja, U. A numerical algorithm for solving higher-order nonlinear BVPs with an application on fluid flow over a shrinking permeable infinite long cylinder. (English) Zbl 1398.65178 Complexity 2018, Article ID 8269541, 11 p. (2018). MSC: 65L10 35Q30 PDFBibTeX XMLCite \textit{L. Y. Al Sakkaf} et al., Complexity 2018, Article ID 8269541, 11 p. (2018; Zbl 1398.65178) Full Text: DOI
Al Khawaja, U.; Al-Mdallal, Qasem M. Convergent power series of \(\operatorname{sech}(x)\) and solutions to nonlinear differential equations. (English) Zbl 1487.34056 Int. J. Differ. Equ. 2018, Article ID 6043936, 10 p. (2018). MSC: 34A34 34A25 41A58 PDFBibTeX XMLCite \textit{U. Al Khawaja} and \textit{Q. M. Al-Mdallal}, Int. J. Differ. Equ. 2018, Article ID 6043936, 10 p. (2018; Zbl 1487.34056) Full Text: DOI
Estévez Schwarz, Diana; Lamour, René A new approach for computing consistent initial values and Taylor coefficients for DAEs using projector-based constrained optimization. (English) Zbl 1409.65049 Numer. Algorithms 78, No. 2, 355-377 (2018). Reviewer: Alan L. Andrew (Bundoora) MSC: 65L80 34A09 90C30 90C55 PDFBibTeX XMLCite \textit{D. Estévez Schwarz} and \textit{R. Lamour}, Numer. Algorithms 78, No. 2, 355--377 (2018; Zbl 1409.65049) Full Text: DOI
Tan, Guangning; Nedialkov, Nedialko S.; Pryce, John D. Conversion methods for improving structural analysis of differential-algebraic equation systems. (English) Zbl 1485.34065 BIT 57, No. 3, 845-865 (2017). MSC: 34A09 65L80 68W30 PDFBibTeX XMLCite \textit{G. Tan} et al., BIT 57, No. 3, 845--865 (2017; Zbl 1485.34065) Full Text: DOI arXiv Link
McKenzie, Ross; Pryce, John Structural analysis based dummy derivative selection for differential algebraic equations. (English) Zbl 1371.65074 BIT 57, No. 2, 433-462 (2017). Reviewer: Kai Diethelm (Braunschweig) MSC: 65L80 34A09 PDFBibTeX XMLCite \textit{R. McKenzie} and \textit{J. Pryce}, BIT 57, No. 2, 433--462 (2017; Zbl 1371.65074) Full Text: DOI
Tan, Guangning; Nedialkov, Nedialko S.; Pryce, John D. Symbolic-numeric methods for improving structural analysis of differential-algebraic equation systems. (English) Zbl 1357.65108 Bélair, Jacques (ed.) et al., Mathematical and computational approaches in advancing modern science and engineering. Based on the international conference on applied mathematics, modeling and computational science, AMMCS, jointly held with the annual meeting of the Canadian applied and industrial mathematics, CAIMS, June 7–15, 2015. Cham: Springer (ISBN 978-3-319-30377-2/hbk; 978-3-319-30379-6/ebook). 763-773 (2016). MSC: 65L80 34A09 68W30 PDFBibTeX XMLCite \textit{G. Tan} et al., in: Mathematical and computational approaches in advancing modern science and engineering. Based on the international conference on applied mathematics, modeling and computational science, AMMCS, jointly held with the annual meeting of the Canadian applied and industrial mathematics, CAIMS, June 7--15, 2015. Cham: Springer. 763--773 (2016; Zbl 1357.65108) Full Text: DOI arXiv
Abad, A.; Barrio, R.; Marco-Buzunariz, M.; Rodríguez, M. Automatic implementation of the numerical Taylor series method: a Mathematica and Sage approach. (English) Zbl 1410.65243 Appl. Math. Comput. 268, 227-245 (2015). MSC: 65L05 PDFBibTeX XMLCite \textit{A. Abad} et al., Appl. Math. Comput. 268, 227--245 (2015; Zbl 1410.65243) Full Text: DOI
Nedialkov, Nedialko S.; Pryce, John D.; Tan, Guangning Algorithm 948: DAESA – a Matlab tool for structural analysis of differential-algebraic equations: software. (English) Zbl 1371.65075 ACM Trans. Math. Softw. 41, No. 2, Article No. 12, 14 p. (2015). MSC: 65L80 65Y15 34A09 PDFBibTeX XMLCite \textit{N. S. Nedialkov} et al., ACM Trans. Math. Softw. 41, No. 2, Article No. 12, 14 p. (2015; Zbl 1371.65075) Full Text: DOI
Pryce, John D.; Nedialkov, Nedialko S.; Tan, Guangning DAESA – a Matlab tool for structural analysis of differential-algebraic equations: theory. (English) Zbl 1371.65076 ACM Trans. Math. Softw. 41, No. 2, Article No. 9, 20 p. (2015). MSC: 65L80 65Y15 34A09 PDFBibTeX XMLCite \textit{J. D. Pryce} et al., ACM Trans. Math. Softw. 41, No. 2, Article No. 9, 20 p. (2015; Zbl 1371.65076) Full Text: DOI
Tan, Guangning; Nedialkov, Nedialko S.; Pryce, John D. A simple method for quasilinearity analysis of DAEs. (English) Zbl 1332.34018 Cojocaru, Monica G. (ed.) et al., Interdisciplinary topics in applied mathematics, modeling and computational science. Selected papers based on the presentations at the 2nd conference, AMMCS 2013, Waterloo, Canada, August 26–30, 2013. Cham: Springer (ISBN 978-3-319-12306-6/hbk; 978-3-319-12307-3/ebook). Springer Proceedings in Mathematics & Statistics 117, 445-450 (2015). MSC: 34A09 PDFBibTeX XMLCite \textit{G. Tan} et al., Springer Proc. Math. Stat. 117, 445--450 (2015; Zbl 1332.34018) Full Text: DOI
Pryce, J.; Nedialkov, N.; Tan, G.; McKenzie, R. Exploiting block triangular form for solving DAEs: reducing the number of initial values. (English) Zbl 1331.65113 Cojocaru, Monica G. (ed.) et al., Interdisciplinary topics in applied mathematics, modeling and computational science. Selected papers based on the presentations at the 2nd conference, AMMCS 2013, Waterloo, Canada, August 26–30, 2013. Cham: Springer (ISBN 978-3-319-12306-6/hbk; 978-3-319-12307-3/ebook). Springer Proceedings in Mathematics & Statistics 117, 367-373 (2015). MSC: 65L80 65L05 34A09 65Y15 PDFBibTeX XMLCite \textit{J. Pryce} et al., Springer Proc. Math. Stat. 117, 367--373 (2015; Zbl 1331.65113) Full Text: DOI
Abad, Alberto; Barrio, Roberto; Blesa, Fernando; Rodríguez, Marcos Algorithm 924, TIDES, a Taylor series integrator for differential equations. (English) Zbl 1295.65138 ACM Trans. Math. Softw. 39, No. 1, Article No. 5, 28 p. (2012). MSC: 65Y15 65D25 65L05 PDFBibTeX XMLCite \textit{A. Abad} et al., ACM Trans. Math. Softw. 39, No. 1, Article No. 5, 28 p. (2012; Zbl 1295.65138) Full Text: DOI
Bervillier, C. Status of the differential transformation method. (English) Zbl 1246.65107 Appl. Math. Comput. 218, No. 20, 10158-10170 (2012). MSC: 65L05 PDFBibTeX XMLCite \textit{C. Bervillier}, Appl. Math. Comput. 218, No. 20, 10158--10170 (2012; Zbl 1246.65107) Full Text: DOI arXiv
Lamour, René; März, Roswitha Detecting structures in differential algebraic equations: computational aspects. (English) Zbl 1246.65138 J. Comput. Appl. Math. 236, No. 16, 4055-4066 (2012). MSC: 65L80 34A09 PDFBibTeX XMLCite \textit{R. Lamour} and \textit{R. März}, J. Comput. Appl. Math. 236, No. 16, 4055--4066 (2012; Zbl 1246.65138) Full Text: DOI
Konguetsof, A. A hybrid method with phase-lag and derivatives equal to zero for the numerical integration of the Schrödinger equation. (English) Zbl 1304.65170 J. Math. Chem. 49, No. 7, 1330-1356 (2011). MSC: 65L05 65L06 PDFBibTeX XMLCite \textit{A. Konguetsof}, J. Math. Chem. 49, No. 7, 1330--1356 (2011; Zbl 1304.65170) Full Text: DOI
Lamour, René; Monett, Dagmar A new algorithm for index determination in DAEs using algorithmic differentiation. (English) Zbl 1226.65073 Numer. Algorithms 58, No. 2, 261-292 (2011). MSC: 65L80 34A09 65D25 68W30 PDFBibTeX XMLCite \textit{R. Lamour} and \textit{D. Monett}, Numer. Algorithms 58, No. 2, 261--292 (2011; Zbl 1226.65073) Full Text: DOI
Barrio, R.; Rodríguez, M.; Abad, A.; Blesa, F. Breaking the limits: The Taylor series method. (English) Zbl 1219.65064 Appl. Math. Comput. 217, No. 20, 7940-7954 (2011). MSC: 65L05 34A34 34A25 65L70 34-04 65Y15 PDFBibTeX XMLCite \textit{R. Barrio} et al., Appl. Math. Comput. 217, No. 20, 7940--7954 (2011; Zbl 1219.65064) Full Text: DOI
Nguyen-Ba, Truong; Hao, Han; Yagoub, Hemza; Vaillancourt, Rémi One-step 9-stage Hermite-Birkhoff-Taylor DAE solver of order 10. (English) Zbl 1215.65129 J. Appl. Math. Comput. 35, No. 1-2, 363-378 (2011). MSC: 65L06 65D05 65D30 PDFBibTeX XMLCite \textit{T. Nguyen-Ba} et al., J. Appl. Math. Comput. 35, No. 1--2, 363--378 (2011; Zbl 1215.65129) Full Text: DOI
Konguetsof, A. Two-step high order hybrid explicit method for the numerical solution of the Schrödinger equation. (English) Zbl 1198.81092 J. Math. Chem. 48, No. 2, 224-252 (2010). MSC: 81Q05 81T80 65L06 PDFBibTeX XMLCite \textit{A. Konguetsof}, J. Math. Chem. 48, No. 2, 224--252 (2010; Zbl 1198.81092) Full Text: DOI
Simos, T. E. Exponentially and trigonometrically fitted methods for the solution of the Schrödinger equation. (English) Zbl 1192.65111 Acta Appl. Math. 110, No. 3, 1331-1352 (2010). MSC: 65L10 34B05 34L40 PDFBibTeX XMLCite \textit{T. E. Simos}, Acta Appl. Math. 110, No. 3, 1331--1352 (2010; Zbl 1192.65111) Full Text: DOI
Konguetsof, A. A new two-step hybrid method for the numerical solution of the Schrödinger equation. (English) Zbl 1200.81051 J. Math. Chem. 47, No. 2, 871-890 (2010). MSC: 81Q05 81T80 81-08 34L40 PDFBibTeX XMLCite \textit{A. Konguetsof}, J. Math. Chem. 47, No. 2, 871--890 (2010; Zbl 1200.81051) Full Text: DOI
Vlachos, D. S.; Anastassi, Z. A.; Simos, T. E. High order phase fitted multistep integrators for the Schrödinger equation with improved frequency tolerance. (English) Zbl 1200.81057 J. Math. Chem. 46, No. 4, 1009-1049 (2009). MSC: 81Q05 81T80 34L40 81-08 PDFBibTeX XMLCite \textit{D. S. Vlachos} et al., J. Math. Chem. 46, No. 4, 1009--1049 (2009; Zbl 1200.81057) Full Text: DOI arXiv
Anastassi, Z. A.; Vlachos, D. S.; Simos, T. E. A family of Runge-Kutta methods with zero phase-lag and derivatives for the numerical solution of the Schrödinger equation and related problems. (English) Zbl 1200.81045 J. Math. Chem. 46, No. 4, 1158-1171 (2009). MSC: 81Q05 34L40 81T80 81-08 65L06 PDFBibTeX XMLCite \textit{Z. A. Anastassi} et al., J. Math. Chem. 46, No. 4, 1158--1171 (2009; Zbl 1200.81045) Full Text: DOI arXiv
Panopoulos, G. A.; Anastassi, Z. A.; Simos, T. E. Two optimized symmetric eight-step implicit methods for initial-value problems with oscillating solutions. (English) Zbl 1198.81099 J. Math. Chem. 46, No. 2, 604-620 (2009). MSC: 81Q05 81V45 34L40 81T80 PDFBibTeX XMLCite \textit{G. A. Panopoulos} et al., J. Math. Chem. 46, No. 2, 604--620 (2009; Zbl 1198.81099) Full Text: DOI arXiv
Nedialkov, Nedialko S.; Pryce, John D. Solving differential algebraic equations by Taylor series. III: The DAETs code. (English) Zbl 1188.65111 JNAIAM, J. Numer. Anal. Ind. Appl. Math. 3, No. 1-2, 61-80 (2008). MSC: 65L80 34A09 65L05 41A58 PDFBibTeX XMLCite \textit{N. S. Nedialkov} and \textit{J. D. Pryce}, JNAIAM, J. Numer. Anal. Ind. Appl. Math. 3, No. 1--2, 61--80 (2008; Zbl 1188.65111)