Borri, Alessandro; Carravetta, Francesco; Palumbo, Pasquale Quadratized Taylor series methods for ODE numerical integration. (English) Zbl 07736280 Appl. Math. Comput. 458, Article ID 128237, 18 p. (2023). MSC: 65Lxx 34Axx 65Dxx PDFBibTeX XMLCite \textit{A. Borri} et al., Appl. Math. Comput. 458, Article ID 128237, 18 p. (2023; Zbl 07736280) Full Text: DOI
Hernandez, Kevin; Elgohary, Tarek A.; Turner, James D.; Junkins, John L. A novel analytic continuation power series solution for the perturbed two-body problem. (English) Zbl 1451.70012 Celest. Mech. Dyn. Astron. 131, No. 10, Paper No. 48, 32 p. (2019). MSC: 70F05 70H09 PDFBibTeX XMLCite \textit{K. Hernandez} et al., Celest. Mech. Dyn. Astron. 131, No. 10, Paper No. 48, 32 p. (2019; Zbl 1451.70012) Full Text: DOI
Groza, Ghiocel; Razzaghi, Mohsen Approximation of solutions of polynomial partial differential equations in two independent variables. (English) Zbl 1403.35018 J. Comput. Appl. Math. 346, 205-223 (2019). MSC: 35A35 35G20 41A10 41A58 PDFBibTeX XMLCite \textit{G. Groza} and \textit{M. Razzaghi}, J. Comput. Appl. Math. 346, 205--223 (2019; Zbl 1403.35018) 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
Rodríguez, Marcos; Blesa, Fernando; Barrio, Roberto OpenCL parallel integration of ordinary differential equations: applications in computational dynamics. (English) Zbl 1380.65476 Comput. Phys. Commun. 192, 228-236 (2015). MSC: 65Y15 65L06 65P20 65Y05 PDFBibTeX XMLCite \textit{M. Rodríguez} et al., Comput. Phys. Commun. 192, 228--236 (2015; Zbl 1380.65476) Full Text: DOI
Chang, Shih-Hsiang New algorithms for Taylor coefficients of indefinite integrals and their applications. (English) Zbl 1338.41019 Appl. Math. Comput. 247, 872-879 (2014). MSC: 41A58 65Q30 PDFBibTeX XMLCite \textit{S.-H. Chang}, Appl. Math. Comput. 247, 872--879 (2014; Zbl 1338.41019) Full Text: DOI
Chang, Shih-Hsiang Taylor series method for solving a class of nonlinear singular boundary value problems arising in applied science. (English) Zbl 1337.65095 Appl. Math. Comput. 235, 110-117 (2014). MSC: 65L11 65L10 34B16 PDFBibTeX XMLCite \textit{S.-H. Chang}, Appl. Math. Comput. 235, 110--117 (2014; Zbl 1337.65095) Full Text: DOI
Groza, Ghiocel; Razzaghi, Mohsen A Taylor series method for the solution of the linear initial-boundary-value problems for partial differential equations. (English) Zbl 1350.65110 Comput. Math. Appl. 66, No. 7, 1329-1343 (2013). MSC: 65M99 35K20 35L20 35C10 PDFBibTeX XMLCite \textit{G. Groza} and \textit{M. Razzaghi}, Comput. Math. Appl. 66, No. 7, 1329--1343 (2013; Zbl 1350.65110) 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
Dena, Ángeles; Abad, Alberto; Barrio, Roberto High-precision periodic orbit corrector. (English) Zbl 1253.37076 Giacomoni, Jaques (ed.) et al., Eleventh international conference Zaragoza-Pau on applied mathematics and statistics, Jaca, Spain, September 15–17, 2010. Zaragoza: Prensas Universitarias de Zaragoza (ISBN 978-84-15538-15-8/pbk). Monografías Matemáticas “García de Galdeano” 37, 115-121 (2012). MSC: 37M20 65P20 37C10 37C25 37-04 PDFBibTeX XMLCite \textit{Á. Dena} et al., Monogr. Mat. García Galdeano 37, 115--121 (2012; Zbl 1253.37076)
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
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