Runge-Kutta-Sarafyan Methods and Delay Differential Equations

• Software for Rootfinding and Interpolation Using Runge-Kutta-Sarafyan Methods, Oak Ridge National Laboratory, ORNL-6151, September 1985.
• Rootfinding and Interpolation with Runge-Kutta-Sarafyan Methods, Transactions of the Society for Computer Simulation, Volume 2, Number 3, 1985, pp. 207-218.
• Stability of Some Continuously Imbedded Runge-Kutta Methods of Sarafyan, Computers and Mathematics with Applications, Volume 13, Number 8, 1987, pp. 677-680.
• Stepsize Control for Delay Differential Equations Using a Pair of Continuously Imbedded Runge-Kutta-Sarafyan Methods, Journal of Computational and Applied Mathematics, Volume 31, 1990, pp. 267-275.
• Software for the Numerical Solution of Systems of Functional Differential Equations With State-Dependent Delays, Applied Numerical Mathematics, Volume 9, 1992, pp. 385-401, with K. W. Neves.
• DRKLAG: Solution of Systems of Functional Differential Equations With State Dependent Delays, TR-92-003, Computer Science Department Technical Report Series, Radford University, Radford, Virginia, 1992, with K. W. Neves.
• DRAKE - Continuous Simulation Software for the Solution of Delay Differential Equations on Personal Computers, TR-93-001, Computer Science Department Technical Report Series, Radford University, Radford, Virginia, 1993, with S. P. Corwin.
• Error Estimation and Step Size Control for Delay Differential Equation Solvers Based on Runge-Kutta-Sarafyan Methods, Computers and Mathematics with Applications, Volume 31, Number 6, 1996, pp. 1-11, with S. P. Corwin.
• DKLAG6: Solution of Systems of Functional Differential Equations With State Dependent Delays, TR-96-002, Computer Science Department Technical Report Series, Radford University, Radford, Virginia, 1996, with S. P. Corwin.
• DKLAG6: A Code Based on Continuously Imbedded Sixth Order Runge-Kutta Methods for the Solution of State Dependent Functional Differential Equations, Applied Numerical Mathematics, Volume 24, Numbers 2-3, 1997, pp. 319-330, with S. P. Corwin and D. Sarafyan.
• Effect of Human Response Time on Rocking Instability of a Two--Wheeled Suitcase, Journal of Sound and Vibration, Volume 207, 1997, pp. 617-625, with S. Suherman, R. H. Plaut, and L. T. Watson.
• Event Location for Ordinary Differential Equations, Computers and Mathematics with Applications, Volume 39, 2000, pp. 43-54, with L. F. Shampine.
• Solving DDEs with dde23, Applied Numerical Mathematics, Volume 37, No. 4, June 2001, pp. 441-458, with L. F. Shampine.
• A Friendly Fortran 90 DDE Solver, Applied Numerical Mathematics, submitted, with L. F. Shampine.

Parallel Solution of Partial Differential Equations

• Experiments With Method of Lines Solvers On a Shared Memory Parallel Computer, Advances in Computer Methods for Partial Differential Equations VI, Proceedings of the Sixth IMACS International Symposium on Computer Methods for Partial Differential Equations, Lehigh University, 1987, pp.161-166, with E. Ng and P. G. Tuttle.
• Experiments With An Ordinary Differential Equation Solver in the Parallel Solution of Method of Lines Problems, Journal of Computational and Applied Mathematics, Volume 38, 1991, pp. 231-253, with D. K. Kahaner, et al.
• Experiments With An Ordinary Differential Equation Solver in the Parallel Solution of Method of Lines Problems - Part II, Advances in Computer Methods for Partial Differential Equations VII, R. Vichnevetsky, D. Knight, and G.Richter (eds.), Proceedings of the Seventh IMACS International Symposium on Computer Methods for Partial Differential Equations, Rutgers University, June, 1992, pp. 404-410, with D. K. Kahaner, et al.
• Experiments With An Ordinary Differential Equation Solver in the Parallel Solution of Method of Lines Problems, in Recent Advances in Numerical Methods and Software for ODEs/DAEs/PDEs, World Scientific Press Publishers, 1992, pp. 7-36, with D. K. Kahaner, et al.
• Recent Developments in Parallel Method of Lines Solutions of Partial Differential Equations, Proceedings of the 14th IMACS World Congress on Computational and Applied Mathematics, pp. 1350-1352, Georgia Tech University, Atlanta, Georgia, July 1994, with S. Chu, et al.
• Recent Developments in Parallel Method of Lines Solutions of Partial Differential Equations, Proceedings of the 14th IMACS World Congress on Computational and Applied Mathematics, pp. 1350-1352, Georgia Tech University, Atlanta, Georgia, July 1994, with S. Chu, et al.
• GOOSEPACK: A Paradigm for the Parallel Solution of Method of Lines Problems Using Preconditioned Krylov Methods on Distributed Memory Computers, Third International Congress on Industrial and Applied Mathematics, (Hamburg, Germany, July 1995), Proceedings Volume 1:Numerical Analysis, Scientific Computing, Computer Science, G. Alefeld, O.Mahrenheit, and R. Mennicken (eds.), Akademie Verlag, 1996, pp. 259-263, with S. C. Chu.

Linear Multistep Methods for Ordinary Differential Equations

• Corrector Methods with Increased Ranges of Relative Stability, Computers and Mathematics with Applications, Volume 3, Number 3, 1977, pp. 197-201, with D. J. Rodabaugh.
• Optimally Stable Fifth Order Integration Methods: A Numerical Approach, International Journal of Mathematical Sciences, Volume 1, 1978, pp. 521-537, with D. J. Rodabaugh.
• Adams-Type Methods with Increased Ranges of Stability, Computers and Mathematics with Applications, Volume 4, Number 4, 1978, pp. 349-357, with D. J. Rodabaugh.
• Low-Order A_0-Stable Adams Methods, Journal of Computational and Applied Mathematics, Volume 5, Number 3, 1979, pp. 225-233, with D. J. Rodabaugh.
• A Note on the Relative Efficiencies of Adams Methods, Computers and Mathematics with Applications, Volume 7, Number 5, 1981, pp. 401-403, with D. J. Rodabaugh.
• Predictor and Corrector Methods with Increased Ranges of Relative Stability, Babcock and Wilcox Company, NPGD-TRG-81-9, September 1981.
• Stable Correctors, Babcock and Wilcox Company, NPGD-TRG-81-8, September 1981.
• The Non-Existence of Certain A_0-Stable Adams-Type Correctors, Journal of Computational and Applied Mathematics, Volume 8, Number 3, 1982, pp. 155-157.
• Stiffly Stable Fourth Order Adams Methods, Journal of Computational and Applied Mathematics, Volume 8, Number 4, 1982, pp. 253-256.

Solution of Specific Problems

• COUPLA: Calculation of Coupled Heat Exchanger Performance, Babcock and Wilcox Company, NPGD-TR-78-13, June 1978, with K. W. Turner.
• DSTPGT: Automatic Software for the Numerical Solution of Differential Equations, Babcock and Wilcox Company, NPGD-TM-521, January 1980, with P. G. Tuttle.
• KAPP V1: Digital Code for the Simulation of Primary System Transients in Pressurized Water Reactors, Babcock and Wilcox Company, NPGD-12-1102640-02, August 1980, with P. G. Tuttle, et al.
• UPIFLOD: Upper Plenum and Cold Leg Injection Reflooding Program, Babcock and Wilcox Company, NPGD-TM-591, February 1981, with P. A. Treventi, et al.
• The Evolution of an O.D.E. Solver in an Industrial Environment, Babcock and Wilcox Company, NPGD-TRG-81-5, June 1981, with P. G. Tuttle.
• A Non-Equilibrium Flashing Model for Rapid Pressure Transients, ASME Paper 81-AT-35, 1981, with F. Aguilar.
• Automatic O.D.E. Software for Use in an Industrial Environment, Advances in Computer Methods for Partial Differential Equations X, Proceedings of the Tenth IMACS World Congress on Systems Simulation and Scientific Computation, August 1982, pp. 440-442, with P. G. Tuttle. Also appears in Modeling and Simulation in Engineering, W. F. Ames (ed.), pp. 53-56.
• Understanding DSTPGT: An Introduction to the Numerical Solution of Ordinary Differential Equations, Babcock and Wilcox Company, UPGD-TM-8, February 1983.
• OASIS: A Computer Program for Once-Through Steam Generator Analysis with Continuous Space Integration at Steady State, Babcock and Wilcox Company, UPGD-TM-16, March 1983, with A. C. Hutter and K. W. Turner.
• Using STACSL for the Solution of Continuous Simulation Problems, Babcock and Wilcox Company, UPGD-TM-18, May 1983.
• The Babcock & Wilcox STACSL Integration Options in ACSL, Proceedings of the Modular Modeling System (MMS-02) Meeting, New Orleans, Louisiana, September 1984, with P. G. Tuttle.
• Event Detection in Continuous Simulation, Proceedings of the International Conference on Power Plant Simulation, Cuernavaca, Morelos, Mexico, November 1984, pp. 341-345, with P. G. Tuttle.
• The Solution of Several Representative Stiff Problems in an Industrial Environment: The Evolution of an O.D.E. Solver, Proceedings of the International Conference on Stiff Computation, Volume 3, April 1982, with P. G. Tuttle. Also appears in Stiff Computation, R. C. Aiken (ed.), Oxford University Press, 1985, pp. 180-193.
• On the Use of CORLIB Subroutines for the Solution of a Model Fluid Flow Problem, Oak Ridge National Laboratory, ORNL-10038, December 1986.
• A Project to Experimentally and Theoretically Examine Fluid Interfacial Wave Phenomena in a Rotating Cylindrical Geometry: Current Results and Future Plans, Oak Ridge National Laboratory, ORNL-6419, September 1987, with W. F.Lawkins, et al.
• On the Use of Rootfinding ODE Software for the Solution of a Common Problem in Nonlinear Dynamical Systems, Proceedings of the International Congress on Computational and Applied Mathematics, July 1988, with D. K. Kahaner and W. F.Lawkins.
• Molecular Dynamics of a Polymer Model on a Hypercube Computer, Computers and Chemistry, Volume 12, Number 1, 1988, pp. 15-20, with J. B. Drake, et al.
• On the Use of Rootfinding ODE Software for the Solution of a Common Problem in Nonlinear Dynamical Systems, Journal of Computational and Applied Mathematics, Volume 28, 1989, pp. 219-230, with D. K. Kahaner and W. F. Lawkins.
• Magnetically Suspended Centrifuge for Studies of Nonlinear Phenomena in Stratified Fluids: Developmental Aspects, American Institute of Physics, Review of Scientific Instruments, Volume 60, Number 10, 1989, pp. 3293-3300, with W. F. Lawkins, et al.
• Solution of State Dependent Systems of Functional Differential Equations, TR-95-001, Computer Science Department Technical Report Series, Radford University, Radford, Virginia, 1995, with S. P. Corwin.

Comparative Mathematical Software Evaluations

• Performance of Vectorized Mathematical Software, Babcock and Wilcox Company, NPGD-TM-346, June 1976, with L. L. Barinka, et al.
• Standard Mathematical Subroutine Library, Babcock and Wilcox Company, NPGD-TM-363, March 1977, with L. L. Barinka, et al.
• A Comparison of Available Software for the Numerical Solution of Stiff Ordinary Differential Equations, Babcock and Wilcox Company, NPGD-TM-368, June 1977.
• Benchmark Fluid Flow Problems for Continuous Simulation Languages, Babcock and Wilcox Company, UPGD-TR-181, September 1984, with P. G. Tuttle.
• Benchmark Fluid Flow Problems for Continuous Simulation Languages, Computers and Mathematics with Applications, Volume 12A, Number 3, 1986, pp. 345-352, with P. G. Tuttle.
• Remarks on the Choice of a Stiff Ordinary Differential Equation Solver for Fluid Flow Problems, Oak Ridge National Laboratory, ORNL-6189, March 1986.
• Remarks on the Choice of a Stiff Ordinary Differential Equation Solver, Computers and Mathematics with Applications, Volume 12A, Number 11, 1986, pp. 1125-1141.
• The Effect of Pivoting in Sparse Ordinary Differential Equation Solvers, Computers and Mathematics with Applications, Volume 12A, Number 12, 1986, pp. 1183-1191.
• A Quantitative Assessment of the Effect of Pivoting in Sparse Ordinary Differential Equation Solvers, Oak Ridge National Laboratory, ORNL-6207, May 1986.
• A Collection of Problems for Testing Rootfinding ODE Solvers, Oak Ridge National Laboratory, ORNL-9912, August 1987.
• Implementation and Evaluation of Several Continuously Imbedded Methods of Sarafyan, ORNL-10434, August 1987.
• Differential Equations Solvers in the SLATEC Mathematical Software Library, Oak Ridge National Laboratory, August 1989.

Friday Night Recreational Stuff

• Thoughts on the Design of Mathematical Software for Use by Industry, Student Communications, Operations Research Society of America, September 1984, with P. G. Tuttle.
• A Bouncing Ball Problem, Problem #1271, Mathematics Magazine, June 1987, p. 179 (problem), June 1988, pp. 202-203 (solution).
• Continuous Simulation on Personal Computers, SIAM News, July 1989.
• On the Zeroes of a Certain Family of Polynomials, Virginia Mathematics Teacher Problem Corner, Problem #45: Volume 20, Number 3, p. 38, Spring, 1994.; Solution: Volume 21, Number 1, pp. 39-41, Fall, 1994.
• An Interesting Property of the Polynomials y = x^{2n+1}, Virginia Mathematics Teacher Problem Corner, Problem #44: Volume 20, Number 3, p. 37, Spring, 1994.; Solution: Volume 21, Number 1, pp. 37-38, Fall, 1994.
• An Inequality Involving the Inverse Cotangent Function, Virginia Mathematics Teacher Problem Corner, Problem #43: Volume 20, Number 3, p. 37, Spring, 1994.; Solution: Volume 21, Number 1, pp. 35-37, Fall, 1994.