Bibliography for Difference Equations

short

 

  1. Analytical formulas for solutions of linear difference equations
    Andruch-Sobilo, Anna
    Appl. Math. E-Notes 5 (2005), 1--9 (electronic), MathSciNet.  
  2. On the z-transform and the nonhomogeneous linear difference equations  
    Taher, R. Ben; El Fetnassi, M.; Rachidi, M.
    J. Interdiscip. Math. 7 (2004), no. 3, 297--313, MathSciNet.  
  3. Global asymptotic stability in a perturbed higher-order linear difference equation
    Pituk, M.  
    Computers and Mathematics with Applications, v 45, n 6-9, March/May, 2003, p 1195-1202, Compendex.  
  4. Construction of a fundamental set of solutions of an arbitrary homogeneous linear difference equation  
    Napoli, A.; Messina, A.; Tretynyk, V.
    XXXIII Symposium on Mathematical Physics (Torún, 2001). Rep. Math. Phys. 49 (2002), no. 2-3, 315--323, MathSciNet.  
  5. Non-linear feedback control of parabolic partial differential difference equation systems
    Antoniades, Charalambos; Christofides, Panagiotis D.
    International Journal of Control, v 73, n 17, Nov 20, 2000, p 1572-1591, Compendex.  
  6. An explicit formula for solutions of some linear difference equation  
    Kwapisz, Marian
    Dedicated to Professor Zenon Moszner on the occasion of his seventieth birthday. Rocznik Nauk.-Dydakt. Prace Mat. No. 17 (2000), 165--170, MathSciNet.  
  7. On the Complete "Discretization" of an nth -Order Linear Differential Equation Model to Obtain the Exact nth-Order Difference Equation Model with Correct "Initial-Sequence Values"
    Johnson C.D.
    Mathematical and Computer Modelling of Dynamical Systems, March 1999, vol. 5, no. 1, pp. 74-84(11), Ingenta.  
  8. On Particular Solutions of Linear Difference Equations with Constant Coefficients  
    Ramesh C. Gupta
    SIAM Review, Vol. 40, No. 3 (Sep., 1998), pp. 680-684, Jstor.    
  9. On the Solution of a Second Order Linear Homogeneous Difference Equation with Variable Coefficients
    Mallik, Ranjan K., Ladas R.G.K.
    Journal of Mathematical Analysis and Applications, 1 November 1997, vol. 215, no. 1, pp. 32-47(16), Ingenta.  
  10. On the Asymptotic Stability of a Class of Linear Difference Equations
    Vassilis G. Papanicolaou
    Mathematics Magazine, Vol. 69, No. 1 (Feb., 1996), pp. 34-43, Jstor.    
  11. The Linear q-Difference Equation y(x) = ay(qx) + f(x)
    Liu Y.-K.
    Applied Mathematics Letters, (Jan., 1995), vol. 8, no. 1, pp. 15-18(4), Ingenta.  
  12. On Linear Difference Equations with Constant Coefficients: An Alternative to the Method of Undetermined Coefficients
    R. C. Gupta
    Mathematics Magazine, Vol. 67, No. 2 (Apr., 1994), pp. 131-135, Jstor.    
  13. Representation of the solution of the nth order linear difference equation with variable coefficients
    Kit Kittappa, R.
    Linear Algebra and Its Applications, v 193, Nov 1, 1993, p 211, Compendex.  
  14. Asymptotic behavior of solutions of a linear second-order difference equation
    Trench, W.F.
    Journal of Computational and Applied Mathematics, v 41, n 1-2, Aug 20, 1992, p 95, Compendex.  
  15. Stability of IPA derivative estimates through a stochastic linear difference equation
    Glasserman, Paul  
    Proceedings of the IEEE Conference on Decision and Control, v 2, 1991, p 1161-1162, Compendex.  
  16. Pursuing Analogies between Differential Equations and Difference Equations
    David L. Abrahamson
    The American Mathematical Monthly, Vol. 96, No. 9 (Nov., 1989), pp. 827-831, Jstor.    
  17. One Expression for the Solutions of Second Order Difference Equations  
    Jerzy Popenda
    Proceedings of the American Mathematical Society, Vol. 100, No. 1 (May, 1987), pp. 87-93, Jstor.    
  18. Riccati type transformations for second-order linear difference equations. II  
    Kwong, Man Kam; Hooker, John W.; Patula, William T.
    J. Math. Anal. Appl. 107 (1985), no. 1, 182--196, MathSciNet.  
  19. A Laplace-like method for solving linear difference equations  
    Gameiro Pais, A.
    Aequationes Math. 27 (1984), no. 1-2, 49--56, MathSciNet.  
  20. Differential and Difference Equations
    Renfrey B. Potts
    The American Mathematical Monthly, Vol. 89, No. 6 (Jun., 1982), pp. 402-407, Jstor.   
  21. Difference Equation Analysis Of Non-Linear Subharmonic And Superharmonic Oscillations  
    Krishnan, A.  
    Journal of Sound and Vibration, v 79, n 1, Nov 8, 1981, p 121-131, Compendex.  
  22. Complete Solutions of Linear Difference Equations
    Albert Nijenhuis
    The American Mathematical Monthly, Vol. 87, No. 8 (Oct., 1980), pp. 658-660, Jstor.   
  23. A Note on Olver's Algorithm for the Solution of Second-Order Linear Difference Equations  
    J. R. Cash
    Mathematics of Computation, Vol. 35, No. 151 (Jul., 1980), pp. 767-772, Jstor.    
  24. Graphical Solutions For The Characteristic Roots Of The First Order Linear Differential-Difference Equation
    Sandquist, G. M.; Rogers, V. C.
    Journal of Dynamic Systems, Measurement and Control, Transactions of the ASME, n 1, Mar, 1979, p 37-43, Compendex.  
  25. On Linear Difference Equations
    K. S. Miller
    The American Mathematical Monthly, Vol. 75, No. 6 (Jun., 1968), pp. 630-632, Jstor.   
  26. Periodic Solutions of Linear Difference Equations  
    Louis Brand
    The American Mathematical Monthly, Vol. 75, No. 1 (Jan., 1968), pp. 51-52, Jstor.   
  27. Difference Equations in Forecasting Formulas  
    J. L. Brenner; D. A. D'Esopo; A. G. Fowler
    Management Science, Vol. 15, No. 3, Theory Series (Nov., 1968), pp. 141-159, Jstor.    
  28. On Existence Theorems for Difference and q-Difference Equations
    Selmo Tauber
    The American Mathematical Monthly, Vol. 73, No. 3 (Mar., 1966), pp. 278-280, Jstor.    
  29. Transform Methods for Difference Equations
    C. A. Grimm; W. Walther
    The American Mathematical Monthly, Vol. 72, No. 7 (Aug., 1965), pp. 747-750, Jstor.   
  30. A Class of Difference Equations with Applications  
    Gerald Berman
    SIAM Review, Vol. 7, No. 4 (Oct., 1965), pp. 513-525, Jstor.    
  31. Existence and Uniqueness Theorems for Solutions of Difference Equations
    Selmo Tauber
    The American Mathematical Monthly, Vol. 71, No. 8 (Oct., 1964), pp. 859-862, Jstor.     
  32. Particular Solutions of Linear Difference Equations with Constant Coefficients  
    C. A. Grimm
    Mathematics Magazine, Vol. 36, No. 1 (Jan., 1963), pp. 54-59, Jstor.  
  33. On Solutions of Homogeneous, Linear, Difference Equations with Constant Coefficients
    David Zeitlin
    The American Mathematical Monthly, Vol. 68, No. 2 (Feb., 1961), pp. 134-137, Jstor.    
  34. A Derivation of the General Solution for Homogeneous, Linear, Difference Equations with Constant Coefficients  
    David Zeitlin
    The American Mathematical Monthly, Vol. 68, No. 4 (Apr., 1961), pp. 369-370, Jstor.    
  35. Particular Solutions for Systems of Nonhomogeneous, Linear Ordinary Difference Equations
    Louis C. Barrett; Richard A. Jacobson
    The American Mathematical Monthly, Vol. 68, No. 9 (Nov., 1961), pp. 911-912, Jstor.    
  36. Particular Solutions for Nonhomogeneous, Linear, Ordinary Difference Equations  
    Louis C. Barrett; Forrest Dristy
    The American Mathematical Monthly, Vol. 67, No. 1 (Jan., 1960), pp. 71-73, Jstor.    
  37. A Matric General Solution of Linear Difference Equations with Constant Coefficients
    Ralph W. Pfouts; C. E. Ferguson
    Mathematics Magazine, Vol. 33, No. 3 (Jan., 1960), pp. 119-127, Jstor.    
  38. Corrections: Linear Differential or Difference Equations with Constant Coefficients
    H. L. Turritin
    The American Mathematical Monthly, Vol. 67, No. 2 (Feb., 1960), p. 161, Jstor.    
  39. Linear Differential or Difference Equations with Constant Coefficients  
    H. L. Turrittin
    The American Mathematical Monthly, Vol. 66, No. 10 (Dec., 1959), pp. 869-875, Jstor.    
  40. Difference Equations and Their Applications
    Louis A. Pipes
    Mathematics Magazine, Vol. 32, No. 5 (May, 1959), pp. 231-246, Jstor.   
  41. A Note on Linear Difference Equations
    R. W. Wagner
    The American Mathematical Monthly, Vol. 65, No. 5 (May, 1958), pp. 351-353, Jstor.  
  42. Some Comments on a Difference Equation
    Harry Levy
    The American Mathematical Monthly, Vol. 63, No. 9 (Nov., 1956), pp. 659-661, Jstor.   
  43. Errata: Linear Difference Equations and the Dirichlet Series Transform  
    Tomlinson Fort
    The American Mathematical Monthly, Vol. 63, No. 2 (Feb., 1956), p. 146, Jstor.    
  44. A Sequence Defined by a Difference Equation  
    Louis Brand
    The American Mathematical Monthly, Vol. 62, No. 7 (Aug., 1955), pp. 489-492, Jstor.   
  45. Linear Difference Equations and the Dirichlet Series Transform  
    Tomlinson Fort
    The American Mathematical Monthly, Vol. 62, No. 9 (Nov., 1955), pp. 641-645, Jstor.    
  46. The Non-Existence of Rational Solutions for Certain Difference Equations
    F. R. Olson
    The American Mathematical Monthly, Vol. 61, No. 3 (Mar., 1954), pp. 179-181, Jstor.    
  47. Difference Equations in Average Value Problems
    E. R. Ott
    The American Mathematical Monthly, Vol. 51, No. 10 (Dec., 1944), pp. 570-578, Jstor.   
  48. On the Explicit Solution of Simultaneous Linear Difference Equations with Constant Coefficients  
    B. Z. Linfield
    The American Mathematical Monthly, Vol. 47, No. 8 (Oct., 1940), pp. 552-554, Jstor.    
  49. Solutions of A Probability Difference Equation  
    Otto Dunkel
    The American Mathematical Monthly, Vol. 32, No. 7 (Aug., 1925), pp. 354-370, Jstor.   

 

 

 

 

 

 

Return to the Numerical Analysis Project

 

Return to the Complex Analysis Project

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2006