Bibliography for Variation of Parameters

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  1. Variational integrators for higher order differential equations
    Sun, Yajuan; Qin, Mengzhao  
    Journal of Computational Mathematics, v 21, n 2, March, 2003, p 135-144, Compendex.
  2. Boundedness in terms of two measures for perturbed systems by generalized variation of parameters.
    Liu, Xinzhi; Shaw, Michael D.
    Commun. Appl. Anal. 5 (2001), no. 4, 435--443, MathSciNet.  
  3. Variational calculus and approximate solutions of differential equations
    Hull, David G.  
    Advances in the Astronautical Sciences, v 108 II, 2001, p 1741-1754, Compendex.
  4. Uniform invariance principle and synchronization. Robustness with respect to parameter variation.
    Rodrigues, H. M.; Alberto, L. F. C.; Bretas, N. G.
    Special issue in celebration of Jack K. Hale's 70th birthday, Part 3 (Atlanta, GA/Lisbon, 1998). J. Differential Equations 169 (2001), no. 1, 228--254, MathSciNet.
  5. Variation of solutions of differential equations of non-integer order with respect to initial condition and parameters.
    Momani, S. M.
    Far East J. Math. Sci. (FJMS) 1 (1999), no. 3, 423--428, MathSciNet.
  6. A generalization of variation of parameters and Lyapunov's method.
    Liu, Xinzhi
    Differential equations with applications to biology (Halifax, NS, 1997), 377--385, Fields Inst. Commun., 21, Amer. Math. Soc., Providence, RI, 1999, MathSciNet.
  7. Method of variation of parameters for dynamic systems.
    Lakshmikantham, V.; Deo, S. G.
    Series in Mathematical Analysis and Applications, 1. Gordon and Breach Science Publishers, Amsterdam, 1998. viii+317 pp., MathSciNet.  
  8. Variation of parameters formulas and maximum principles for linear hyperbolic problems in two independent variables.
    Pandit, Sudhakar G.
    Dynam. Contin. Discrete Impuls. Systems 4 (1998), no. 2, 295--312, MathSciNet.  
  9. Variation of parameters in terms of Lyapunov-like functions and stability of perturbed systems.
    Liu, Xinzhi; Vatsala, A. S.
    Nonlinear Stud. 5 (1998), no. 1, 47--58, MathSciNet.  
  10. A variation of parameters solution of a quasilinear Skorohod SDE using the Wick product.
    Gjessing, Håkon K.
    Stochastic analysis and related topics, VI (Geilo, 1996), 245--249, Progr. Probab., 42, Birkhäuser Boston, Boston, MA, 1998, MathSciNet.  
  11. Variation of parameters formula and Lipschitz stability of nonlinear matrix differential equations.
    Fausett, Donald W.; Köksal, Semen
    World Congress of Nonlinear Analysts '92, Vol. I--IV (Tampa, FL, 1992), 1415--1426, de Gruyter, Berlin, 1996, MathSciNet.
  12. Nonlinear variation of parameters formula for dynamical systems on measure chains.
    Lakshmikantham, V.; Shahzad, N.; Sivasundaram, S.
    Dynam. Contin. Discrete Impuls. Systems 1 (1995), no. 2, 255--265, MathSciNet.  
  13. Variation of solutions of stochastic differential equations with respect to the initial condition and parameters.
    Ouknine, Y.
    Random Oper. Stochastic Equations 2 (1994), no. 1, 99--101, MathSciNet.
  14. Nonlinear variation of parameter methods for summary difference equations in several independent variables.
    Sheng, Qin; Agarwal, Ravi P.
    Appl. Math. Comput. 61 (1994), no. 1, 39--60, MathSciNet.
  15. Method of variation of parameters is not exhausted.
    Samodurov, Alexander; Cvejic, Stana
    Mat. Bilten 42 (1992), no. 16, 81--83, MathSciNet.  
  16. Variation of Parameters Formula for the Equation of Cooke and Wiener  
    K. N. Jayasree; S. G. Deo  
    Proceedings of the American Mathematical Society, Vol. 112, No. 1. (May, 1991), pp. 75-80, Jstor.  
  17. A new approach to the method of nonlinear variation of parameters for a perturbed nonlinear neutral functional-differential equation.
    Ventura, A.
    J. Math. Anal. Appl. 138 (1989), no. 1, 59--74, MathSciNet.  
  18. Bifurcation of saddle-node and separatrix cycle with the variation of the parameter in a certain quadratic differential system.
    Ye, Yan Qian; Ye, Wei Yin; Artés, J. C.
    Ann. Differential Equations 5 (1989), no. 1, 99--106, MathSciNet.
  19. Nonlinear variation of parameters formula for integro-differential equations of Volterra type.
    Hu, Shou Chuan; Lakshmikantham, V.; Rama Mohan Rao, M.
    J. Math. Anal. Appl. 129 (1988), no. 1, 223--230, MathSciNet.  
  20. On some variation of parameter methods for integro-differential, integral, and quasilinear partial integro-differential equations.
    Beesack, Paul R.
    Appl. Math. Comput. 22 (1987), no. 2-3, 189--215, MathSciNet.  
  21. A variation of parameters formula for Burgers system.
    Fitzgibbon, W. E.
    Infinite-dimensional systems (Retzhof, 1983), 78--85, Lecture Notes in Math., 1076, Springer, Berlin, 1984, MathSciNet.  
  22. Integral formulae associated with non-parameter-invariant multiple integral problems of arbitrary order in the calculus of variations.  
    Berry, Thomas G.; Venter, Sarel
    Aequationes Math.  21  (1980), no. 2-3, 200--224, MathSciNet.
  23. Richard A new approach to the method of nonlinear variation of parameters.
    Lord, M. E.; Mitchell, A.
    Appl. Math. Comput. 4 (1978), no. 2, 95--105, MathSciNet.  
  24. A variation of parameters approach to the arbitrarily torqued, asymmetric rigid body problem.
    Kraige, L. G.; Skaar, S. B.
    J. Astronaut. Sci. 25 (1977), no. 3, 207--226, MathSciNet.  
  25. Compléments au traité de Kamke. XIV. Applications of the variation of parameters method to nonlinear second order differential equations.
    Mitrinovic, Dragoslav S.; Keckic, Jovan D.
    Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. Fiz. No. 544--576 (1976), 3--7, MathSciNet.  
  26. Additions to Kamke's treatise. VII. Variation of parameters for nonlinear second order differential equations.
    Keckic, Jovan D.
    Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. Fiz. No. 544--576 (1976), 31--36, MathSciNet.  
  27. Parameter Variation For The Solution Of Two-Point Boundary-Value Problems And Applications In The Calculus Of Variations.
    Glasser, D.; de Villiers, N.  
    Journal of Optimization Theory and Applications, v 13, n 2, Feb, 1974, p 164-178, Compendex.
  28. A variation-of-parameters inequality.
    Lovelady, David Lowell
    Proc. Amer. Math. Soc. 26 (1970), 598--602, MathSciNet.  
  29. Modification of the variation-of-parameters method and integration of the Schrödinger equation.
    Tani, Smio; Inokuti, Mitio
    J. Computational Phys. 11 (1973), 409--422, MathSciNet.  
  30. Variation of Parameters for Nonlinear Differential-Difference Equations  
    Stuart P. Hastings  
    Proceedings of the American Mathematical Society, Vol. 19, No. 5. (Oct., 1968), pp. 1211-1216, Jstor.
  31. A general method of variation of parameters for numerical integration.
    Goodyear, W. H.
    Astronom. J. 70 1965 524--526, MathSciNet.  
  32. Application of the method of variation of parameters to the approximate calculation of exponential functions of a real matrix. (Ukrainian)
    Davidenko, D. F.
    Dopovidi Akad. Nauk Ukraïn. RSR 1964 1964 158--163, MathSciNet.  
  33. A Note on the Method of Variation of Parameters (in Classroom Notes)  
    P. Chadwick  
    The American Mathematical Monthly, Vol. 69, No. 4. (Apr., 1962), pp. 291-293, Jstor.  
  34. On the Method of Variation of Parameters--II (in Mathematical Notes)  
    David Zeitlin  
    The American Mathematical Monthly, Vol. 67, No. 9. (Nov., 1960), pp. 869-871, Jstor.  
  35. Parameter Variation and the Solution of Bernoulli's Equation (in Classroom Notes)  
    K. Venkannayah  
    The American Mathematical Monthly, Vol. 66, No. 5. (May, 1959), pp. 409-410, Jstor.
  36. On the Method of Variation of Parameters (in Classroom Notes)  
    David Zeitlin  
    The American Mathematical Monthly, Vol. 66, No. 4. (Apr., 1959), pp. 300-302, Jstor.
  37. The method of variation of parameters as applied to the computation of eigenvalues and eigenvectors of matrices.
    Davidenko, D. F.
    Dokl. Akad. Nauk SSSR 131 1007--1010 (Russian); translated as Soviet Math. Dokl. 1 1960 364--367, MathSciNet.  
  38. The Geometry of Variation of Parameters (in Classroom Notes)  
    R. M. Conkling  
    The American Mathematical Monthly, Vol. 64, No. 8. (Oct., 1957), pp. 589-591, Jstor.
  39. Construction of the Green's Function of a Linear Differential System  
    Kenneth S. Miller  
    Mathematics Magazine, Vol. 26, No. 1. (Sep. - Oct., 1952), pp. 1-8, Jstor.   

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2004