Freihet, Asad; Hasan, Shatha; Al-Smadi, Mohammed; Gaith, Mohamed; Momani, Shaher Construction of fractional power series solutions to fractional stiff system using residual functions algorithm. (English) Zbl 1458.34017 Adv. Difference Equ. 2019, Paper No. 95, 15 p. (2019). MSC: 34A08 65L04 34A25 PDFBibTeX XMLCite \textit{A. Freihet} et al., Adv. Difference Equ. 2019, Paper No. 95, 15 p. (2019; Zbl 1458.34017) 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
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
El-Ajou, Ahmad; Abu Arqub, Omar; Al-Smadi, Mohammed A general form of the generalized Taylor’s formula with some applications. (English) Zbl 1338.40007 Appl. Math. Comput. 256, 851-859 (2015). MSC: 40A25 PDFBibTeX XMLCite \textit{A. El-Ajou} et al., Appl. Math. Comput. 256, 851--859 (2015; Zbl 1338.40007) Full Text: DOI
Estévez Schwarz, Diana; Lamour, René Projector based integration of DAEs with the Taylor series method using automatic differentiation. (English) Zbl 1301.65087 J. Comput. Appl. Math. 262, 62-72 (2014). MSC: 65L80 65D25 PDFBibTeX XMLCite \textit{D. Estévez Schwarz} and \textit{R. Lamour}, J. Comput. Appl. Math. 262, 62--72 (2014; Zbl 1301.65087) 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
Rodríguez, Marcos; Barrio, Roberto Reducing rounding errors and achieving Brouwer’s law with Taylor series method. (English) Zbl 1243.65080 Appl. Numer. Math. 62, No. 8, 1014-1024 (2012). MSC: 65L05 34A34 65Y20 65L70 34A25 PDFBibTeX XMLCite \textit{M. Rodríguez} and \textit{R. Barrio}, Appl. Numer. Math. 62, No. 8, 1014--1024 (2012; Zbl 1243.65080) Full Text: DOI
Thelwell, Roger J.; Warne, Paul G.; Warne, Debra A. Cauchy-Kowalevski and polynomial ordinary differential equations. (English) Zbl 1242.34017 Electron. J. Differ. Equ. 2012, Paper No. 11, 8 p. (2012). MSC: 34A25 34A12 35A10 PDFBibTeX XMLCite \textit{R. J. Thelwell} et al., Electron. J. Differ. Equ. 2012, Paper No. 11, 8 p. (2012; Zbl 1242.34017) Full Text: EMIS
Barrio, R.; Rodríguez, M.; Abad, A.; Serrano, S. Uncertainty propagation or box propagation. (English) Zbl 1235.65092 Math. Comput. Modelling 54, No. 11-12, 2602-2615 (2011). MSC: 65L99 PDFBibTeX XMLCite \textit{R. Barrio} et al., Math. Comput. Modelling 54, No. 11--12, 2602--2615 (2011; Zbl 1235.65092) 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
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)
Corless, Robert M.; Ilie, Silvana Polynomial cost for solving IVP for high-index DAE. (English) Zbl 1141.65066 BIT 48, No. 1, 29-49 (2008). MSC: 65L80 65L05 65L70 34A09 PDFBibTeX XMLCite \textit{R. M. Corless} and \textit{S. Ilie}, BIT 48, No. 1, 29--49 (2008; Zbl 1141.65066) Full Text: DOI
Miletics, E.; Molnárka, G. Implicit extension of Taylor series method with numerical derivatives for initial value problems. (English) Zbl 1092.65056 Comput. Math. Appl. 50, No. 7, 1167-1177 (2005). Reviewer: Zdzislaw Jackiewicz (Tempe) MSC: 65L05 65L06 34A34 65L60 65L20 65L70 PDFBibTeX XMLCite \textit{E. Miletics} and \textit{G. Molnárka}, Comput. Math. Appl. 50, No. 7, 1167--1177 (2005; Zbl 1092.65056) Full Text: DOI
Nedialkov, Nedialko S.; Pryce, John D. Solving differential-algebraic equations by Taylor series. I: Computing Taylor coefficients. (English) Zbl 1084.65075 BIT 45, No. 3, 561-591 (2005). Reviewer: Răzvan Răducanu (Iaşi) MSC: 65L80 34A09 68W30 PDFBibTeX XMLCite \textit{N. S. Nedialkov} and \textit{J. D. Pryce}, BIT 45, No. 3, 561--591 (2005; Zbl 1084.65075) Full Text: DOI
Barrio, Roberto Performance of the Taylor series method for ODEs/DAEs. (English) Zbl 1067.65063 Appl. Math. Comput. 163, No. 2, 525-545 (2005). MSC: 65L05 65L80 34A09 34A34 PDFBibTeX XMLCite \textit{R. Barrio}, Appl. Math. Comput. 163, No. 2, 525--545 (2005; Zbl 1067.65063) Full Text: DOI
Nedialkov, N. S.; Jackson, K. R.; Corliss, G. F. Validated solutions of initial value problems for ordinary differential equations. (English) Zbl 0934.65073 Appl. Math. Comput. 105, No. 1, 21-68 (1999). Reviewer: D.Petcu (Timişoara) MSC: 65L05 65L50 34A34 65G20 65G40 PDFBibTeX XMLCite \textit{N. S. Nedialkov} et al., Appl. Math. Comput. 105, No. 1, 21--68 (1999; Zbl 0934.65073) Full Text: DOI
Khan, Ishtiaq Rasool; Ohba, Ryoji Closed-form expressions for the finite difference approximations of first and higher derivatives based on Taylor series. (English) Zbl 0939.65031 J. Comput. Appl. Math. 107, No. 2, 179-193 (1999). Reviewer: R.S.Dahiya (Ames) MSC: 65D25 26-04 PDFBibTeX XMLCite \textit{I. R. Khan} and \textit{R. Ohba}, J. Comput. Appl. Math. 107, No. 2, 179--193 (1999; Zbl 0939.65031) Full Text: DOI