Numerical Solution of Differential Equations by Direct Taylor Expansion
, PP. 623-630 10.4236/jamp.2017.53053
Keywords: Taylor Series, Expansion, Algorithm, Numerical Solution, Differential Equations
A variation of the direct Taylor expansion algorithm is suggested and applied to several linear and nonlinear differential equations of interest in physics and engineering, and the results are compared with those obtained from other algorithms. It is shown that the suggested algorithm competes strongly with other existing algorithms, both in accuracy and ease of application, while demanding a shorter computation time.
[ 1] Press, W.H., Teukolsky, S.A., Vetterling, W.T. and Flannery, B.P. (1992) Numerical Recipes in Fortran. 2nd Edition, Cambridge University Press, Cambridge, Chapter 16.
[ 2] Brauer, F. and Nohel, J.A. (1967) Ordinary Differential Equations. Benjamin, New York, Chapter 8.
[ 3] Carnahan, B., Luther, H.A. and Wilkes, J.O. (1969) Applied Numerical Methods. Wiley, New York, Chapter 6.
[ 4] Gould, H. and Tobochnik, J. (1996) An Introduction to Computer Simulation Methods. 2nd Edition, Addison-Wesley, Read-ing, 120-126.
[ 5] Agnew, R.P. (1960) Differential Equations. 2nd Edition, McGraw-Hill, New York, Chapter 8.
[ 6] Golomb, M. and Shanks, M. (1965) Elements of Ordinary Differential Equations. 2nd Edition, McGraw-Hill, New York, 18-33.
[ 7] Tenenbaum, M. and Pollard, H. (1963) Ordinary Differential Equations. Dover, New York, Chapter 10.
[ 8] Betz, H., Burcham, P.B. and Ewing, G.M. (1964) Differential Equations with Applications. 2nd Edition, Harper and Row, New York, 254-261.
[ 9] Ordinary Differential Equations of Higher Order Can Always Be Reduced to a Set of First-Order Differential Equations (See, for Example, Reference ).
[ 10] An Algorithm Is Called n-th Order if the Global Error Is of the Order of hn.
[ 11] Arfken, G. (1985) Mathematical Methods for Physicists. 3rd Edition, Academic Press, San Diego, 491-492.
[ 12] Gear, C.W. (1971) Numerical Initial Value Problems in Ordinary Differential Equation. Prentice-Hall, Englewood Cliffs, Chapter 2.
[ 13] Lapidus, L. and Seinfeld, J.H. (1971) Numerical Solution of Ordinary Differential Equations. Academic Press, New York, Chapter 2.
[ 14] Boyce, W.E. and DiPrima, R.C. (1967) Elementary Differential Equations and Boundary Value Problems. Wiley, New York, 286-321.
[ 15] Rainville, E.D. and Bedient, P.E. (1981) Elementary Differential Equations. 6th Edition, Macmillan Publishing Company, New York, 409-411.
[ 16] Fowles, G.R. and Cassiday, G.L. (1999) Analytical Mechanics. 6th Edition, Saunders, New York, 132.
[ 17] Baierlein, R. (1983) Newtonian Mechanics. McGraw-Hill, New York, 88-93.
[ 18] Ibid, 81-82.
[ 19] Kittel, C. (1976) Introduction to Solid State Physics. 5th Edition, Wiley, New York, 81.
[ 20] Lebedev, N.N. (1972) Special Functions and Their Applications. Translated and Edited by Silverman R.A., Dover, New York.
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