Ordinary differential

Gear C W 1971 Numerical Initial Value Problems in Ordinary Differential Equations (Englewood Cliffs, NJ Prentice-Hall)... 

Shampine S 1994 Numerical Solutions of Ordinary Differential Equations (New York Chapman and Hall)... 

Gear C W 1966 The numerical integration of ordinary differential equations of various orders ANL 7126... 

J. A. McCammon, B. M. Pettitt, and L. R. Scott. Ordinary differential equa tions of molecular dynamics. Computers Math. Applic., 28 319-326, 1994. 

E. Hairer and G. Wanner. Solving Ordinary Differential Equations II. Stiff and Differential-Algebraic Problems, volume 14 of Springer Series in Computational Mathematics. Springer-Verlag, New York, New York, second edition, 1996. 

L.R. Petzold, L.O. Jay, and J. Yen. Numerical solution of highly oscillatory ordinary differential equations. Acta Numerica, pages 437-484, 1997. 

Verlet, L. Computer Experiments" on Classical Fluids. I. Thermodynamical Properties of Lennard-Jones Molecules. Physical Review 159 (1967) 98-103 Janezic, D., Merzel, F. Split Integration Symplectic Method for Molecular Dynamics Integration. J. Chem. Inf. Comput. Sci. 37 (1997) 1048-1054 McLachlan, R. I. On the Numerical Integration of Ordinary Differential Equations by Symplectic Composition Methods. SIAM J. Sci. Comput. 16 (1995) 151-168... 

W. Gautschi. Numerical integration of ordinary differential equations based on trigonometric polynomials. Numer. Math., 3 381-397, 1961. 

Before attempting to answer this question, let us first summarize the procedure of section 11.3 in a slightly modified form. Equations (11.20) and (11.21) provide a set of simultaneous ordinary differential equations to determine the pressure and the composition, represented by mole fractions Xi,..,Xn in terms of the dummy variable. If at least one of the x s varies monotonically with X, so that its derivative never vanishes, we may use this x in place of X as an Independent variable. Without loss of generality this x may be labelled x, so we may divide equation (11.20) and each equation (11.21) for r = 2,...,n-l, by equation (11.21)... 

These ordinary differential equations may then be solved for p,, ... 

The remaining terms in equation set (4.125) are identical to their counterparts derived for the steady-state case (given as Equations (4.55) to (4.60)). By application of the 9 time-stepping method, described in Chapter 2, Section 2.5, to the set of first-order ordinary differential equations (4.125) the working equations of the solution scheme are obtained. The general form of tliese equations will be identical to Equation (2.111) in Chapter 2,... 

Numerical Solution of Ordinary Differential Equations as Initial... 

Ordinary Differential Equations-Boundary Value Problems. 3-57... 

Gear, G. W. Numerical Initial Value Frohlems in Ordinary Differential Equations, Prentice Hall, Englewood CBffs, NJ (1971). 

Hindmarsh, A. C. GEARB Solution of Ordinary Differential Equations Having Banded Jacobian, UCID-.30059, Rev. 1 Computer Documentation, Lawrence Livermore Laboratory, University of California (1975). 

Lamhert, J. D. Computational Methods in Ordinary Differential Equations, Wiiey New York (1973). 

Lapidus, L., and J. Seinfeld. Numerical Solution of Ordinary Differential Equations, Academic, New York (1971). 

Smith, I. M., J. L. Siemienivich, and I. Gladweh. A Comparison of Old and New Methods for Large Systems of Ordinary Differential Equations Arising from Parabolic Partial Differential Equations, Num. Anal. Rep. Department of Engineering, no. 13, University of Manchester, England (1975). 

References Ordinary Differential Equations Elementary level, 41, 44, 62,... 

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