Bibliography for Separable Differential Equations

unabridged

 

  1. Interval systems of max-separable linear equations
    Cechlarova K.; Cuninghame-Green R.A.
    Linear Algebra and its Applications, 1 January 2002, vol. 340, no. 1, pp. 215-224(10), Ingenta.   
  2. Verhulst's Logistic Curve  
    David M. Bradley
    College Math Journal: Volume 32, Number 2, 2001, Pages: 94-98.
  3. Complex second-order differential equations and separability
    Sarlet, W.; Thompson, G.  
    Applicable Algebra in Engineering, Communications and Computing, v 11, n 5, 2001, p 333-357, Compendex.
  4. Math Bite: Once in a While, Differentiation Is Multiplicative  
    J. Marshall Ash
    Mathematics Magazine: Volume 73, Number 4, 2000, Pages: 302.  
  5. On separable Schrödinger equations.
    Zhdanov, Renat; Zhalij, Alexander
    J. Math. Phys. 40 (1999), no. 12, 6319--6338, MathSciNet.
  6. Separation of variables for the 1-dimensional non-linear diffusion equation
    Philip W. Doyle and Peter J. Vassiliou
    International Journal of Non-Linear Mechanics, Volume 33, Issue 2, March 1998, Pages 315-326
  7. Complete separability of time-dependent second-order ordinary differential equations
    Cantrijn, F.; Sarlet, W.; Vandecasteele, A.; Martinez, E.  
    Acta Applicandae Mathematicae, v 42, n 3, Mar, 1996, p 309-334, Compendex.
  8. Exponential stability of nonlinear delay systems with separable variables. (Chinese)
    Wang, Mei Juan
    Gongcheng Shuxue Xuebao 13 (1996), no. 4, 15--20, MathSciNet.
  9. Optimal rho parameter for the ADI iteration for the separable diffusion equation in three dimensions.
    Ma, Sangback
    Commun. Korean Math. Soc. 10 (1995), no. 1, 39--48, MathSciNet.
  10. Matrix decomposition algorithms in orthogonal spline collocation for separable elliptic boundary value problems.
    Bialecki, Bernard; Fairweather, Graeme
    SIAM J. Sci. Comput. 16 (1995), no. 2, 330--347, MathSciNet.
  11. Geometric characterization of separable second-order differential equations.
    Martínez, Eduardo; Cariñena, José F.; Sarlet, Willy
    Math. Proc. Cambridge Philos. Soc. 113 (1993), no. 1, 205--224, MathSciNet.
  12. Families of separable partial differential equations.
    Costa, G.B.; Levine, L.E.
    International journal of mathematical education in science and technology, 1993, vol. 24, no. 5, pp. 631, Ingenta.
  13. Alternating Direction Collocation for Separable Elliptic Partial Differential Equations  
    K. D. Cooper, P. M. Prenter  
    SIAM Journal on Numerical Analysis, Vol. 28, No. 3. (Jun., 1991), pp. 711-727, Jstor.  
  14. Alternating direction collocation for separable elliptic partial differential equations.
    Cooper, K. D.; Prenter, P. M.
    SIAM J. Numer. Anal. 28 (1991), no. 3, 711--727, MathSciNet.
  15. A program for solving separable elliptic equations; algorithm 685.
    Kaufman, Linda.; Warner, Daniel D.
    ACM Transactions on Mathematical Software v. 16 (Dec. 1990) p. 325-51
  16. Exploiting the separability in the solution of systems of linear ordinary differential equations
    Å. Björck and Z. Zlatev
    Computers & Mathematics with Applications, v 18, n 5, 1989, p 421-438, Compendex.
  17. A Projection Method for the Numerical Solution of Linear Systems in Separable Stiff Differential Equations.
    Lopez, L.; Trigiante, D.
    International journal of computer mathematics, 1989, vol. 30, no. 3/4, pp. 191, Ingenta.
  18. Factorisation of separable partial differential equations.
    Humi, Mayer
    J. Phys. A 20 (1987), no. 14, 4577--4585, MathSciNet.
  19. Formulas for solutions of differential equations. II. Formulas for solutions of separable variables of higher-order linear partial differential equations with variable coefficients. (Chinese)
    Wang, Cun Zheng
    Acta Math. Appl. Sinica 10 (1987), no. 1, 43--54, MathSciNet.
  20. When is an Ordinary Differential Equation Separable? (in Notes)  
    David Scott  
    American Mathematical Monthly, Vol. 92, No. 6. (Jun. - Jul., 1985), pp. 422-423, Jstor.  
  21. High-Order, Fast-Direct Methods for Separable Elliptic Equations  
    Linda Kaufman, Daniel D. Warner  
    SIAM Journal on Numerical Analysis, Vol. 21, No. 4. (Aug., 1984), pp. 672-694, Jstor.  
  22. A Direct Method for the Discrete Solution of Separable Elliptic Equations  
    Paul N. Swarztrauber  
    SIAM Journal on Numerical Analysis, Vol. 11, No. 6. (Dec., 1974), pp. 1136-1150, Jstor.  
  23. Swarztrauber, Paul N.
    A direct method for the discrete solution of separable elliptic equations.
    SIAM J. Numer. Anal. 11 (1974), 1136--1150, MathSciNet.
  24. A note on non-separable solutions of linear partial differential equations.
    Chakrabarti, Aloknath
    J. Math. Anal. Appl. 42 (1973), 198--204, MathSciNet.
  25. Some Separable Forms of the Riccati Equation (in Mathematical Notes)  
    P. R. P. Rao, V. H. Ukidave  
    American Mathematical Monthly, Vol. 75, No. 1. (Jan., 1968), pp. 38-39, Jstor.  
  26. Chebyshev methods for separable partial differential equations.
    Mason, J. C.
    1969 Information Processing 68 (Proc. IFIP Congress, Edinburgh, 1968), Vol. 1: Mathematics, Software pp. 164--169 North-Holland, Amsterdam, MathSciNet.
  27. Quasi-separable solutions of systems of partial differential equations. I. Elliptic case.
    Levin, S.; Martin, M. H.
    1965 Simpos. Internaz. Appl. Anal. Fis. Mat. (Cagliari-Sassari, 1964) pp. 84--96 Edizioni Cremonese, Rome, MathSciNet.
  28. Iterative procedures for solving finite-difference approximations to separable partial differential equations.
    Osborne, M. R.
    Comput. J. 6 1963/1964 93--99, MathSciNet.
  29. Operational methods for separable differential equations.
    Friedman, Bernard
    1961 Modern mathematics for the engineer: Second series pp. 51--67 McGraw-Hill, New York, MathSciNet.
  30. Unrestricted Solution Fields of Almost Separable Differential Equations  
    Philip Hartman  
    Transactions of the American Mathematical Society, Vol. 63, No. 3. (May, 1948), pp. 560-580, Jstor.  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2004