Armadillo, Tommaso; Bonciani, Roberto; Devoto, Simone; Rana, Narayan; Vicini, Alessandro Evaluation of Feynman integrals with arbitrary complex masses via series expansions. (English) Zbl 1523.81077 Comput. Phys. Commun. 282, Article ID 108545, 15 p. (2023). MSC: 81Q30 55P35 81S40 41A58 32D15 81V05 PDFBibTeX XMLCite \textit{T. Armadillo} et al., Comput. Phys. Commun. 282, Article ID 108545, 15 p. (2023; Zbl 1523.81077) Full Text: DOI arXiv
Tritt, Alex; Morris, Joshua; Hochstetter, Joel; Anderson, R. P.; Saunderson, James; Turner, L. D. Spinsim: a GPU optimized Python package for simulating spin-half and spin-one quantum systems. (English) Zbl 1521.81500 Comput. Phys. Commun. 287, Article ID 108701, 12 p. (2023). MSC: 81V72 81Q05 35Q41 41A58 65D30 81Q93 81-10 PDFBibTeX XMLCite \textit{A. Tritt} et al., Comput. Phys. Commun. 287, Article ID 108701, 12 p. (2023; Zbl 1521.81500) Full Text: DOI arXiv
Wu, Weilei; Tang, Bin Performance analysis of a geometrically nonlinear isolation system subjected to high levels of excitation. (English) Zbl 1503.70014 Appl. Math. Modelling 108, 612-628 (2022). MSC: 70K40 PDFBibTeX XMLCite \textit{W. Wu} and \textit{B. Tang}, Appl. Math. Modelling 108, 612--628 (2022; Zbl 1503.70014) Full Text: DOI
Koepf, Wolfram Computer algebra. An algorithm-oriented introduction. Translated and updated from the 2006 German language edition. (English) Zbl 1484.68004 Springer Undergraduate Texts in Mathematics and Technology. Cham: Springer (ISBN 978-3-030-78016-6/hbk; 978-3-030-78019-7/pbk; 978-3-030-78017-3/ebook). xii, 384 p. (2021). Reviewer: Andreas Maletti (Leipzig) MSC: 68-01 68W30 PDFBibTeX XMLCite \textit{W. Koepf}, Computer algebra. An algorithm-oriented introduction. Translated and updated from the 2006 German language edition. Cham: Springer (2021; Zbl 1484.68004) Full Text: DOI
Hou, Qing-hu; Li, Guojie Log-concavity of \(P\)-recursive sequences. (English) Zbl 1466.05008 J. Symb. Comput. 107, 251-268 (2021). MSC: 05A20 05A10 41A60 41A58 PDFBibTeX XMLCite \textit{Q.-h. Hou} and \textit{G. Li}, J. Symb. Comput. 107, 251--268 (2021; Zbl 1466.05008) Full Text: DOI arXiv
Freihet, A. A.; Zuriqat, M. Analytical solution of fractional Burgers-Huxley equations via residual power series method. (English) Zbl 1483.35318 Lobachevskii J. Math. 40, No. 2, 174-182 (2019). MSC: 35R11 35C10 65M99 PDFBibTeX XMLCite \textit{A. A. Freihet} and \textit{M. Zuriqat}, Lobachevskii J. Math. 40, No. 2, 174--182 (2019; Zbl 1483.35318) Full Text: DOI
Sharma, J. R.; Arora, H. Efficient higher order derivative-free multipoint methods with and without memory for systems of nonlinear equations. (English) Zbl 1499.65192 Int. J. Comput. Math. 95, No. 5, 920-938 (2018). MSC: 65H10 65Y20 41A58 PDFBibTeX XMLCite \textit{J. R. Sharma} and \textit{H. Arora}, Int. J. Comput. Math. 95, No. 5, 920--938 (2018; Zbl 1499.65192) Full Text: DOI
Bhalla, S.; Kumar, S.; Argyros, I. K.; Behl, Ramandeep A family of higher order derivative free methods for nonlinear systems with local convergence analysis. (English) Zbl 1413.65200 Comput. Appl. Math. 37, No. 5, 5807-5828 (2018). MSC: 65H10 41A58 65Y20 PDFBibTeX XMLCite \textit{S. Bhalla} et al., Comput. Appl. Math. 37, No. 5, 5807--5828 (2018; Zbl 1413.65200) Full Text: DOI
Navas-Palencia, Guillermo High-precision computation of the confluent hypergeometric functions via Franklin-Friedman expansion. (English) Zbl 1393.33008 Adv. Comput. Math. 44, No. 3, 841-859 (2018). MSC: 33C15 33F05 41A58 65D20 68W30 PDFBibTeX XMLCite \textit{G. Navas-Palencia}, Adv. Comput. Math. 44, No. 3, 841--859 (2018; Zbl 1393.33008) Full Text: DOI
Wojas, Włodzimierz; Krupa, Jan Some remarks on Taylor’s polynomials visualization using Mathematica in context of function approximation. (English) Zbl 1383.97008 Kotsireas, Ilias S. (ed.) et al., Applications of computer algebra, Kalamata, Greece, July 20–23, 2015. Cham: Springer (ISBN 978-3-319-56930-7/hbk; 978-3-319-56932-1/ebook). Springer Proceedings in Mathematics & Statistics 198, 487-498 (2017). MSC: 97I40 97I30 97U70 41A10 65D18 PDFBibTeX XMLCite \textit{W. Wojas} and \textit{J. Krupa}, Springer Proc. Math. Stat. 198, 487--498 (2017; Zbl 1383.97008) Full Text: DOI
Pearson, John W.; Olver, Sheehan; Porter, Mason A. Numerical methods for the computation of the confluent and Gauss hypergeometric functions. (English) Zbl 1360.33009 Numer. Algorithms 74, No. 3, 821-866 (2017). Reviewer: Peter Massopust (München) MSC: 33C05 33C15 41A58 41A60 PDFBibTeX XMLCite \textit{J. W. Pearson} et al., Numer. Algorithms 74, No. 3, 821--866 (2017; Zbl 1360.33009) Full Text: DOI arXiv Link
Kowalenko, Victor The partition method for a power series expansion. Theory and applications. (English) Zbl 1371.41001 Amsterdam: Elsevier/Academic Press (ISBN 978-0-12-804466-7/hbk; 978-0-12-804511-4/ebook). ix, 302 p. (2017). Reviewer: Neha Malik (New Delhi) MSC: 41-02 41A58 05-02 05A17 05C85 11P81 11P82 40A20 PDFBibTeX XMLCite \textit{V. Kowalenko}, The partition method for a power series expansion. Theory and applications. Amsterdam: Elsevier/Academic Press (2017; Zbl 1371.41001) Full Text: Link
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
Sharma, Janak Raj; Arora, Himani A novel derivative free algorithm with seventh order convergence for solving systems of nonlinear equations. (English) Zbl 1320.65077 Numer. Algorithms 67, No. 4, 917-933 (2014). Reviewer: Vasilis Dimitriou (Chania) MSC: 65H10 65Y20 41A58 PDFBibTeX XMLCite \textit{J. R. Sharma} and \textit{H. Arora}, Numer. Algorithms 67, No. 4, 917--933 (2014; Zbl 1320.65077) Full Text: DOI
Ozer, Okan; Koklu, Halide; Resitoglu, Serap Application of the asymptotic Taylor expansion method to bistable potentials. (English) Zbl 1292.81056 Adv. Math. Phys. 2013, Article ID 239254, 8 p. (2013). MSC: 81Q10 81Q05 41A58 PDFBibTeX XMLCite \textit{O. Ozer} et al., Adv. Math. Phys. 2013, Article ID 239254, 8 p. (2013; Zbl 1292.81056) Full Text: DOI arXiv
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
Levy, Martin S.; Cochran, James J.; Golnabi, Saeed A moment preserving finitization across the power series family of probability distributions. (English) Zbl 1241.60008 Commun. Stat., Theory Methods 41, No. 4-6, 653-664 (2012). MSC: 60E05 62E17 PDFBibTeX XMLCite \textit{M. S. Levy} et al., Commun. Stat., Theory Methods 41, No. 4--6, 653--664 (2012; Zbl 1241.60008) Full Text: DOI
Wang, Pengfei; Li, Jianping; Li, Qian Computational uncertainty and the application of a high-performance multiple precision scheme to obtaining the correct reference solution of Lorenz equations. (English) Zbl 1232.65106 Numer. Algorithms 59, No. 1, 147-159 (2012). MSC: 65L05 34A34 34A25 PDFBibTeX XMLCite \textit{P. Wang} et al., Numer. Algorithms 59, No. 1, 147--159 (2012; Zbl 1232.65106) Full Text: DOI
Costabile, F.; Napoli, A. A Mathematica package for the solution of IVPs. (English) Zbl 1264.65103 Int. J. Numer. Methods Appl. 6, No. 2, 123-136 (2011). MSC: 65L05 34A34 34A25 65Y15 PDFBibTeX XMLCite \textit{F. Costabile} and \textit{A. Napoli}, Int. J. Numer. Methods Appl. 6, No. 2, 123--136 (2011; Zbl 1264.65103) Full Text: Link
Lampret, Vito The higher derivatives of the inverse tangent function revisited. (English) Zbl 1255.65064 Appl. Math. E-Notes 11, 224-231 (2011). Reviewer: Manfred Tasche (Rostock) MSC: 65D25 65D20 41A58 33B10 33F05 PDFBibTeX XMLCite \textit{V. Lampret}, Appl. Math. E-Notes 11, 224--231 (2011; Zbl 1255.65064) 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
Kowalenko, Victor Properties and applications of the reciprocal logarithm numbers. (English) Zbl 1208.11032 Acta Appl. Math. 109, No. 2, 413-437 (2010). Reviewer: Thomas Stoll (Marseille) MSC: 11B73 41A58 05A17 05C90 PDFBibTeX XMLCite \textit{V. Kowalenko}, Acta Appl. Math. 109, No. 2, 413--437 (2010; Zbl 1208.11032) Full Text: DOI
Pal, Srimanta Numerical methods. Principles, analysis and algorithms. (English) Zbl 1196.65001 Oxford: Oxford University Press (ISBN 978-0-19-569375-1/pbk). xii, 812 p. (2009). Reviewer: Georg Hebermehl (Berlin) MSC: 65-01 65Fxx 65Lxx 65Mxx 65Nxx 65Yxx 65D05 65D07 65D30 65G50 65H04 65H05 65H10 92B20 97M50 00A06 65C05 65R20 PDFBibTeX XMLCite \textit{S. Pal}, Numerical methods. Principles, analysis and algorithms. Oxford: Oxford University Press (2009; Zbl 1196.65001)
Costabile, F.; Napoli, A. Solving BVPs using two-point Taylor formula by a symbolic software. (English) Zbl 1134.65047 J. Comput. Appl. Math. 210, No. 1-2, 136-148 (2007). MSC: 65L10 34B15 PDFBibTeX XMLCite \textit{F. Costabile} and \textit{A. Napoli}, J. Comput. Appl. Math. 210, No. 1--2, 136--148 (2007; Zbl 1134.65047) Full Text: DOI
Youssef, I. K.; El-Arabawy, H. A. Picard iteration algorithm combined with Gauss-Seidel technique for initial value problems. (English) Zbl 1122.65369 Appl. Math. Comput. 190, No. 1, 345-355 (2007). MSC: 65L05 34A34 65L06 68W30 65L20 PDFBibTeX XMLCite \textit{I. K. Youssef} and \textit{H. A. El-Arabawy}, Appl. Math. Comput. 190, No. 1, 345--355 (2007; Zbl 1122.65369) Full Text: DOI
Higham, Nicholas J.; Smith, Matthew I. Computing the matrix cosine. (English) Zbl 1033.65027 Numer. Algorithms 34, No. 1, 13-26 (2003). MSC: 65F30 15A54 PDFBibTeX XMLCite \textit{N. J. Higham} and \textit{M. I. Smith}, Numer. Algorithms 34, No. 1, 13--26 (2003; Zbl 1033.65027)
Evans, Neil D.; Chappell, Michael J. Extensions to a procedure for generating locally identifiable reparameterisations of unidentifiable systems. (English) Zbl 0989.93021 Math. Biosci. 168, No. 2, 137-159 (2000). Reviewer: Yves Cherruault (Paris) MSC: 93B30 68W30 PDFBibTeX XMLCite \textit{N. D. Evans} and \textit{M. J. Chappell}, Math. Biosci. 168, No. 2, 137--159 (2000; Zbl 0989.93021) Full Text: DOI
Nagle, R. Kent; Saff, Edward B.; Snider, Arthur David Fundamentals of differential equations and boundary value problems. 3rd ed. (English) Zbl 0949.34001 Reading, MA: Addison-Wesley. xxii, 859 p., 61 p. appendix (2000). MSC: 34-01 35-01 34Axx 34Bxx PDFBibTeX XMLCite \textit{R. K. Nagle} et al., Fundamentals of differential equations and boundary value problems. 3rd ed. Reading, MA: Addison-Wesley (2000; Zbl 0949.34001)
Chen, C. S.; Muleshkov, A. S.; Golberg, M. A. The numerical evaluation of particular solutions for Poisson’s equation – a revisit. (English) Zbl 0972.65097 Brebbia, C. A. (ed.) et al., Boundary elements. XXI. Papers from the 21st international conference on the boundary element method, Oxford, Great Britain, August 1999. Southampton: WIT Press. Int. Ser. Adv. Bound. Elem. 6, 313-322 (1999). MSC: 65N35 35J05 65Y15 68W30 PDFBibTeX XMLCite \textit{C. S. Chen} et al., Adv. Bound. Elem. 6, 313--322 (1999; Zbl 0972.65097)
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
Strampp, Walter Higher mathematics with Mathematica. Vol. 2: Analysis. (Höhere Mathematik mit Mathematica. Band 2: Analysis.) (German) Zbl 0865.00008 Lehrbuch Computeralgebra. Wiesbaden: Vieweg. viii, 328 p. (1997). Reviewer: H.-J.Kowalsky (Braunschweig) MSC: 00A06 26-01 PDFBibTeX XMLCite \textit{W. Strampp}, Höhere Mathematik mit Mathematica. Band 2: Analysis. Wiesbaden: Vieweg (1997; Zbl 0865.00008)
Glinos, Nikolaos Designing an algorithm for the series solution of \(n\)th order linear ODE’s with polynomial coefficients. (English) Zbl 1065.65087 Keränen, Veikko (ed.) et al., Innovation in mathematics. Proceedings of the 2nd international Mathematica symposium, Rovaniemi, Finland, July 1997. Southampton: CMP, Computational Mechanics Publications (ISBN 1-85312-505-9). 161-168 (1997). MSC: 65L05 34A30 68W30 PDFBibTeX XMLCite \textit{N. Glinos}, in: Innovation in mathematics. Proceedings of the 2nd international \(Mathematica\) symposium, Rovaniemi, Finland, July 1997. Southampton: CMP, Computational Mechanics Publications. 161--168 (1997; Zbl 1065.65087)
Lustig, Steven R.; Rastogi, Sanjeev; Wagner, Norman Telescoping fast multipole methods using Chebyshev economization. (English) Zbl 0842.70002 J. Comput. Phys. 122, No. 2, 317-322 (1995). MSC: 70-08 70F10 68W30 PDFBibTeX XMLCite \textit{S. R. Lustig} et al., J. Comput. Phys. 122, No. 2, 317--322 (1995; Zbl 0842.70002) Full Text: DOI
Wray, Jonathan; Green, Gary G. R. Calculation of the Volterra kernels of nonlinear dynamic systems using an artificial neural network. (English) Zbl 0805.92002 Biol. Cybern. 71, No. 3, 187-195 (1994). MSC: 92B20 41A58 93C10 PDFBibTeX XMLCite \textit{J. Wray} and \textit{G. G. R. Green}, Biol. Cybern. 71, No. 3, 187--195 (1994; Zbl 0805.92002) Full Text: DOI
Koepf, Wolfram Taylor polynomials of implicit functions, of inverse functions, and of solutions of ordinary differential equations. (English) Zbl 0817.41001 Complex Variables, Theory Appl. 25, No. 1, 23-33 (1994). Reviewer: T.D.Narang (Amritsar) MSC: 41-04 68W30 68-04 30B10 30-04 PDFBibTeX XMLCite \textit{W. Koepf}, Complex Variables, Theory Appl. 25, No. 1, 23--33 (1994; Zbl 0817.41001) Full Text: DOI Link
Koepf, Wolfram Power series in computer algebra. (English) Zbl 0758.30026 J. Symb. Comput. 13, No. 6, 581-603 (1992). Reviewer: F.Schwarz (Paderborn) MSC: 30D30 30B10 68W30 30D05 PDFBibTeX XMLCite \textit{W. Koepf}, J. Symb. Comput. 13, No. 6, 581--603 (1992; Zbl 0758.30026) Full Text: DOI
Ioakimidis, N. I. Semi-numerical iterative series solution of linear algebraic equations with “MATHEMATICA”. (English) Zbl 0757.65033 Commun. Appl. Numer. Methods 8, No. 7, 421-429 (1992). Reviewer: J.Zítko (Praha) MSC: 65F10 68W30 PDFBibTeX XMLCite \textit{N. I. Ioakimidis}, Commun. Appl. Numer. Methods 8, No. 7, 421--429 (1992; Zbl 0757.65033) Full Text: DOI