Integer Interval Value of Milne’s Predictor and Milne’s Corrector Method for First Order ODE
About this article
Keywords:
Interval analysis, Milnes predictor and corrector method, first order differential equation, ect..Abstract
In this paper A new approaches to solve the approximate solution of the initial value problem for the first order ordinary
differential equations and the solution can be used to compute y numerically specified the value of near to in the
interval analysis method and also used Milne’s predictor and corrector for interval. In interval method gives a more accurate the
approximate solution of life situation and numerical illustration are given
References
[1] Karl Nickel, On the Newton method in Interval Analysis. Technical report 1136, Mathematical Research Center, University of Wiscon-sion, Dec1971
[2] Hansen E. R (1988), An overview of Global Optimization using interval analysis in Moore(1988) pp 289-307
[3] E. R. Hansen, “Global Optimization Using Interval Analysis”, Mar-cel Dekker, Inc., New York, 1992
[4] Helmut Ratschek and Jon G. Rlkne, New Computer Methods for Global Optimization, Wiley, New York, 1988
[5] K. Ganesan and P. Veeramani, On Arithmetic Operations of Inter-val Numbers, International Journal of Uncertainty, Fuzziness and Knowledge - Based Systems, 13 (6) (2005), 619 - 631
View more references (20)
[6] G.Veeramalai and R.J.Sundararaj, “Single Variable Unconstrained Optimization Techniques Using Interval Analysis” IOSR Journal of Mathematics (IOSR-JM), ISSN: 2278-5728. Volume 3,Issue 3, (Sep-Oct. 2012), PP 30-34
[7] G.Veeramalai, ”Unconstrained Optimization Techniques Using Fuzzy Non Linear Equations” Asian Academic Research Journal of Multi-Disciplinary,ISSN: 2319- 2801.Volume 1, Issue 9, (May2013), PP 58-67
[8] Eldon Hansen, Global optimization using interval analysis- Marcel Dekker, 1992
[9] Hansen E. R (1979), “Global optimization using interval analysis-the one dimensional case, J.Optim, Theory Application, 29, 314-331
[10] G.Veeramalai and P.Gajendran, ”A New Approaches to Solving Fuzzy Linear System with Interval Valued Triangular Fuzzy Num-ber” Indian Scholar An International Multidisciplinary Research e-Journal , ISSN: 2350-109X,.Volume 2, Issue 3, (Mar2016), PP 31-38
[11] G.Veeramalai, “Eigen Values of an Interval Matrix” CLEAR IJRMST, Vol-02-No-03, Jan-June 2012, ISSN: 2249-3492
[12] Louis B. Rall, A Theory of interval iteration, proceeding of the American Mathematics Society, 86z:625-631, 1982
[13] Louis B. Rall, Application of interval integration to the solution of integral equations. Journal of Integral equations 6: 127-141,1984
[14] Ramon E. Moore, R. Baker Kearfoth, Michael J. Cloud, Introduc-tion to interval analysis, SIAM, 105-127, Philadelphia, 2009
[15] Hansen E.R (1978a), “ Interval forms of Newton’s method, Com-puting 20, 153-163
[16] K. Ganesan, On Some Properties of Interval Matrices, International Journal of Computational and Mathematical Sciences, 1 (2) (2007), 92-99
[17] E. R. Hansen and R. R. Smith, Interval arithmetic in matrix compu-tations, Part 2, SIAM. journal of Numerical Analysis, 4 (1967), 1 – 9
[18] E. R. Hansen, On the solution of linear algebraic equations with in-terval coefficients, Linear Algebra Appl, 2 (1969), 153 – 165
[19] E. R. Hansen, Bounding the solution of interval linear Equations, SIAM Journal of Numerical Analysis, 29 (5) (1992), 1493 – 1503
[20] P. Kahl, V. Kreinovich, A. Lakeyev and J. Rohn, Computational complexity and feasibility of data processing and interval computa-tions Kluwer Academic Publishers, Dordrecht (1998)
[21] S. Ning and R. B. Kearfott, A comparison of some methods for solving linear interval Equations, SIAM Journal of Numerical Anal-ysis, 34 (1997),1289 – 1305
[22] R. E. Moore, Methods and Applications of Interval Analysis, SIAM, Philadelphia, 1979
[23] E. R. Hansen and R. R. Smith, “Interval arithmetic in matrix com-putations”, Part 2, SI AM. Journal of Numerical Analysis, vol. 4, pp.1 – 9, 1967
[24] A. Neumaier, “Interval Methods for Systems of Equations”, Cam-bridge University Press, Cambridge, 1990
[25] Moore, R.E.: Interval Analysis. Prentice-Hall, Englewood Cliffs (1966)