The List of Publications by Alexander Gofen (1981-present)

The Modern Taylor Method, Elementary Functions, the Unifying View

1. Fast Taylor-Series Expansion and the Solution of the Cauchy Problem. U.S.S.R. Comput. Maths. Math. Phys. Vol. 22, No. 5, pp. 74-88 (1982)

2. Guaranteed Bounds for General and Remainder Terms for Taylor Series Expansion of Solutions of Cauchy Problem. Differential Equations, Vol. 20, No. 7, pp. 859-869 (1984)

3. Taylor Method of Integrating Ordinary Differential Equations: the Problem of Steps and Singularities. Cosmic Research, Vol. 30, No. 6, pp. 581-593 (1992)

4. The Taylor Center for PCs: Exploring, Graphing and Integrating ODEs with the Ultimate Accuracy. In: P.M.A. Sloot et al. (Eds), Computational Science - ICCS 2002, LNCS 2329, pp. 562-571, Amsterdam, Springer.

5. ODEs and Redefining the Concept of Elementary Functions. In: P.M.A. Sloot et al. (Eds), Computational Science - ICCS 2002, LNCS 2329, pp. 1000-1009, Amsterdam, Springer.

6. The Taylor Center Demo for PCs. http://www.taylorcenter.org/gofen/TaylorMethod.htm 

7. Interactive Environment for the Taylor Integration (in 3D Stereo). In: Hamid R. Arabnia et al., (Eds), Proceedings of the 2005 International Conference on Scientific Computing (CSC 05),  pp. 67-73, Las Vegas, Nevada, CSREA Press.

8. Visual Environment for the Taylor integration in 3D Stereo. In: Proceedings DMS 2007, the 13th Intern. Conf. on Distributed Multimedia Systems, pp. 251-255

9. Unremovable "removable" singularities. Complex Variables and Elliptic Equations, Vol. 53, No. 7, July 2008, pp. 633-642

10. The ordinary differential equations and automatic differentiation unified. Complex Variables and Elliptic Equations, Vol. 54, No. 9, September 2009, pp. 825-854

11. Using the Taylor Center to Teach ODEs, CODEE Journal: Vol. 9, Article 6, 2012.


12. The Unifying View on Ordinary Differential Equations and Automatic Differentiation, yet with a Gap to Fill. The 9th AIMS Conference on Dynamical Systems, Differential Equations and Applications, Orlando, Florida, July 1 - 5, 2012. Registration ID: 1351, special session SS39, pass code SS652Gofen


13. Powers Which Commute or Associate as Solutions of ODEs. Teaching Mathematics and Computer Science, 11/2, 2013, p. 241-254.


14. Report about the situation with gap in the Unifying View (2021)


15. The Taylor Center ODEs Solver as a Generator of Simulations.  SIMODE 2024. (Day 2, 5:00 pm)


Research by others employing the Taylor Cetner software


1. Richard Montgomery. "Dropping bodies" in "The Mathematical Intelligencer", 2023.



2. Mark Frenkel et al. The Continuous Measure of Symmetry as a Dynamic Variable…

    Symmetry 2023, 15, 2153. https://doi.org/10.3390/sym15122153


Teaching materials with the Exploratorium – the Virtual Lab-works


1. Exploratorium: Lab Works in Applied ODEs


2. Rigid body motion: the three cases


3. A remarkable mapping into the shape space (w1w2w3) and shape sphere (u1u2u3) for the 3-body problem


4. Three body free fall periodic orbits: new remarkable features 


Visual Science Programming

1. (With M. MacKeben)  An introduction to accurate display timing for PCs under "Windows". Spatial Vision, Vol. 10, No. 4, pp. 361-368 (1997)

2. (With M. MacKeben) The physiological blind spot as a marker for eccentric viewing. Invest Ophthal Vis Sci. Vol. 42, No. 4, p. 4580. (2001)

3. (With M. MacKeben and D. Fletcher) How patients scan images after foveal vision loss: scanning efficiency and SLO analysis of scanning eye movements. Vision 2005, ISLRR, London, International Congress Series Elsevier, London.

4. (With M. MacKeben) Gaze-Contingent display for retinal function testing by scanning laser ophthalmoscope. J. Opt. Soc. Am., Vol. 24, No. 5, pp. 1402-1410 (2007)



Pascal and Delphi

1. From Pascal to Delphi to Object Pascal-2000. ACM SIGPLAN Notices, Vol. 36, No. 6, pp. 38-49 (2001).

2. Object vs. Class: Fewer Pointers, Less Double Thinking. Delphi Informant Magazine, Vol. 5, No. 7, pp. 47-52 (1999).

3. Dynamic Arrays. Delphi Informant Magazine, Vol. 6, No. 2,  (2000).

4. Recursion Excursion. Delphi Informant Magazine, Vol. 6, No. 8, pp. 30-38 (2000).

5. A Recursive Journey to the Problem of Three Bodies. Delphi Informant Magazine. Vol. 8, No. 3, pp. 44-49, (2002)

6. 3D Delphi: Stereo Vision on Your Home PC. Delphi Informant Magazine. Vol. 10, No. 1, pp. 8-15, (2004)

7. Do-It-Yourself 3D. Delphi Informant Magazine. Vol. 10, No. 8, pp. 17-22, (2004)

Philosophy of Science

1. My philosophy in a straight talk

2. Will computers ever take the power?  (In Russian)


1. (With S. Belousov) On the Organization of Computerized Data Archives of Meteorological Fields Analysis Derived During FGGE. Meteorology and Hydrology, 1981, No. 2, pp. 103‑107.

2. The Screen System Supporting Software Design and Documentation Based on Nassi-Schneiderman Structures Techniques. In: Proceedings of the Simferopol Conference, 1988, pp. 183-185.

3. (With co-authors) The Functions of the Software in the Authoring System RADUGA for Computer Aided Training. In: Proceedings of the Simferopol Conference, 1988, pp. 137-139.

4. Dialog Systems for Computer Aided Training. In: Informatics and Computer Literacy (Ed. B. Naumov), 1988, pp. 176-186