Ernsthausen, John M.; Nedialkov, Nedialko S. Stepsize selection in the rigorous defect control of Taylor series methods. (English) Zbl 1429.65145 J. Comput. Appl. Math. 368, Article ID 112483, 10 p. (2020). MSC: 65L05 34A34 41A58 65G20 65G40 41A10 PDFBibTeX XMLCite \textit{J. M. Ernsthausen} and \textit{N. S. Nedialkov}, J. Comput. Appl. Math. 368, Article ID 112483, 10 p. (2020; Zbl 1429.65145) 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)
Nedialkov, Nedialko S.; Pryce, John D. Solving differential-algebraic equations by Taylor series. II: Computing the system Jacobian. (English) Zbl 1123.65080 BIT 47, No. 1, 121-135 (2007). Reviewer: Răzvan Răducanu (Iaşi) MSC: 65L80 34A09 68W30 65L05 PDFBibTeX XMLCite \textit{N. S. Nedialkov} and \textit{J. D. Pryce}, BIT 47, No. 1, 121--135 (2007; Zbl 1123.65080) 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
Jackson, Kenneth R.; Nedialkov, Nedialko S. Some recent advances in validated methods for IVPs for ODEs. (English) Zbl 0998.65068 Appl. Numer. Math. 42, No. 1-3, 269-284 (2002). MSC: 65L05 65G20 65G40 34A34 65L70 65L20 PDFBibTeX XMLCite \textit{K. R. Jackson} and \textit{N. S. Nedialkov}, Appl. Numer. Math. 42, No. 1--3, 269--284 (2002; Zbl 0998.65068) Full Text: DOI
Nedialkov, Nedialko S.; Jackson, Kenneth R. An interval Hermite-Obreschkoff method for computing rigorous bounds on the solution of an initial value problem for an ordinary differential equation. (English) Zbl 0947.65081 Reliab. Comput. 5, No. 3, 289-310 (1999). MSC: 65L05 34A34 65L70 65G40 PDFBibTeX XMLCite \textit{N. S. Nedialkov} and \textit{K. R. Jackson}, Reliab. Comput. 5, No. 3, 289--310 (1999; Zbl 0947.65081) 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