Bibliography for Elliptic PDE's

short

 

  1. Numerical solution of elliptic partial differential equation using radial basis function neural networks
    Jianyu, Li; Siwei, Luo; Yingjian, Qi; Yaping, Huang
    Neural Networks, v 16, n 5-6, June/July, 2003, p 729-734, Compendex.
  2. Symbolic computation of high order compact difference schemes for three dimensional linear elliptic partial differential equations with variable coefficients
    Ge, Lixin; Zhang, Jun
    Journal of Computational and Applied Mathematics, v 143, n 1, Jun 1, 2002, p 9-27, Compendex.
  3. A new parallel domain decomposition method for the adaptive finite element solution of elliptic partial differential equations
    Bank, R.E.; Jimack, P.K.
    Concurrency Computation Practice and Experience, v 13, n 5, 2001, p 327-350, Compendex.
  4. A complex variable boundary element method for elliptic partial differential equations in a multiple-connected region.
    Ang, W. T.; Kang, Ilwon
    Int. J. Comput. Math. 75 (2000), no. 4, 515--525, MathSciNet.  
  5. Analysis of iterative line spline collocation methods for elliptic partial differential equations.
    Hadjidimos, A.; Houstis, E. N.; Rice, J. R.; Vavalis, E.
    SIAM J. Matrix Anal. Appl. 21 (1999), no. 2, 508--521 (electronic), MathSciNet.  
  6. CVBEM for a system of second-order elliptic partial differential equations
    Ang, W.T.; Park, Y.S.
    Engineering Analysis with Boundary Elements, v 21, n 2, Mar, 1998, p 179-184, Compendex.
  7. Coiflet interpolation and approximate solutions of elliptic partial differential equations.
    Lin, En-Bing; Zhou, Xiaolin
    Numer. Methods Partial Differential Equations 13 (1997), no. 4, 303--320, MathSciNet.  
  8. On the Solvability of a Nonlinear Second-Order Elliptic Equation at Resonance  
    Chung-Cheng Kuo  
    Proceedings of the American Mathematical Society, Vol. 124, No. 1. (Jan., 1996), pp. 83-87, Jstor.  
  9. Boundary element monotone iteration scheme for semilinear elliptic partial differential equations.
    Deng, Yuanhua; Chen, Goong; Ni, Wei-Ming; Zhou, Jianxin
    Math. Comp. 65 (1996), no. 215, 943--982, MathSciNet.  
  10. Multiple Solutions for a Semilinear Elliptic Equation  
    Manuel A. Del Pino; Patricio L. Felmer  
    Transactions of the American Mathematical Society, Vol. 347, No. 12. (Dec., 1995), pp. 4839-4853, Jstor.  
  11. A Remark on Positive Radial Solutions of the Elliptic Equation in Rn  
    Yasuhiro Sasahara; Kazunaga Tanaka  
    Proceedings of the American Mathematical Society, Vol. 123, No. 2. (Feb., 1995), pp. 527-531, Jstor.
  12. A fourth-order finite difference scheme for two-dimensional nonlinear elliptic partial differential equations.    
    Saldanha, Godfrey; Anantha Krishnaiah, U.    
    Numer. Methods Partial Differential Equations 11 (1995), no. 1, 33--40, MathSciNet.   
  13. A Nonlinear Elliptic Equation Arising from Gauge Field Theory and Cosmology  
    Xinfu Chen; Stuart Hastings; J. Bryce McLeod; Yisong Yang  
    Proceedings: Mathematical and Physical Sciences, Vol. 446, No. 1928. (Sep. 8, 1994), pp. 453-478, Jstor.
  14. Quadratic spline collocation methods for elliptic partial differential equations.
    Christara, Christina C.
    BIT 34 (1994), no. 1, 33--61, MathSciNet.  
  15. On the Solution of an Integral Equation Arising in Potential Problems for Circular and Elliptic Disks  
    J. Boersma; E. Danicki  
    SIAM Journal on Applied Mathematics, Vol. 53, No. 4. (Aug., 1993), pp. 931-941, Jstor.
  16. Convergence Analysis of the Schwarz Algorithm and Multilevel Decomposition Iterative Methods II: Nonselfadjoint and Indefinite Elliptic Problems  
    Junping Wang  
    SIAM Journal on Numerical Analysis, Vol. 30, No. 4. (Aug., 1993), pp. 953-970
  17. Near-circularity of the error curve in Chebyshev approximation of solutions to a class of elliptic partial differential equations in the complex plane.
    McCoy, Peter A.
    Computational complex analysis. J. Comput. Appl. Math. 46 (1993), no. 1-2, 315--326, MathSciNet.  
  18. Elliptic partial differential equation and optimal control.
    Zhong, Wan Xie; Zhong, Xiang Xiang
    Numer. Methods Partial Differential Equations 8 (1992), no. 2, 149--169, MathSciNet.  
  19. Mapping of curved surfaces onto a side boundary of the three-dimensional computational grid using two elliptic partial differential equations
    Nakamura, S.; Fradl, D.P.; Spradling, M.L.; Kuwahara, K.
    Proceedings of the International Conference on Numerical Grid Generation in Computational Fluid Dynamics and Related Fields, 1991, p 925, Compendex.
  20. 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.  
  21. On oblique derivative problems for fully nonlinear second-order elliptic partial differential equations on nonsmooth domains
    Dupuis, P.; Ishii, H.
    Nonlinear Analysis, Theory, Methods & Applications, v 15, n 12, 1990, p 1123, Compendex.
  22. Convergence of difference schemes for nonlinear elliptic differential problems which admit Laplace equation.    
    Mosurski, Ryszard    
    Opuscula Math. No. 4 (1988), 181--204 (1989), MathSciNet.   
  23. Convergence of O(h^4) cubic spline collocation methods for elliptic partial differential equations.
    Houstis, E. N.; Vavalis, E. A.; Rice, J. R.
    SIAM J. Numer. Anal. 25 (1988), no. 1, 54--74, MathSciNet.  
  24. The Finite Element Method for a Degenerate Elliptic Equation  
    Donald A. French  
    SIAM Journal on Numerical Analysis, Vol. 24, No. 4. (Aug., 1987), pp. 788-815, Jstor.
  25. A Quasi-Newton Method for Elliptic Boundary Value Problems  
    C. T. Kelley; E. W. Sachs  
    SIAM Journal on Numerical Analysis, Vol. 24, No. 3. (Jun., 1987), pp. 516-531, Jstor.
  26. Accelerated iterative methods for elliptic partial differential equations.  
    Grandek, K.
    Systems Anal. Modelling Simulation  4  (1987),  no. 6, 541--547, MathSciNet.  
  27. On the Elliptic Equation in R2  
    Nichiro Kawano; Takasi Kusano; Manabu Naito  
    Proceedings of the American Mathematical Society, Vol. 93, No. 1. (Jan., 1985), pp. 73-78, Jstor.
  28. Mixed Finite Element Methods for Quasilinear Second-Order Elliptic Problems  
    F. A. Milner  
    Mathematics of Computation, Vol. 44, No. 170. (Apr., 1985), pp. 303-320, Jstor.
  29. The numerical solution of elliptic partial differential equations by the method of lines.
    Edwards, Bruce H.
    Rev. Colombiana Mat. 19 (1985), no. 3-4, 297--312, MathSciNet.  
  30. The Free Boundary of a Semilinear Elliptic Equation  
    Avner Friedman; Daniel Phillips  
    Transactions of the American Mathematical Society, Vol. 282, No. 1. (Mar., 1984), pp. 153-182, Jstor.
  31. 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.
  32. Preconditioned iterative methods for the numerical solution of elliptic partial differential equations.
    Evans, D. J.; Missirlis, N. M.
    Preconditioning methods: analysis and applications, 115--177, Topics in Comput. Math., 1, Gordon & Breach, New York, 1983, MathSciNet.  
  33. Difference methods for elliptic partial differential equations with nonunique solutions.
    Molchanov, I. N.; Galba, E. F.
    SIAM J. Numer. Anal. 19 (1982), no. 3, 531--547, MathSciNet.  
  34. The solution of elliptic partial differential equations by a new block over-relaxation technique.
    Evans, D. J.; Biggins, M. J.
    Internat. J. Comput. Math. 10 (1981/82), no. 3-4, 269--282, MathSciNet.  
  35. Chebyshev expansion methods for the solution of elliptic partial differential equations.
    McKerrell, A.; Phillips, C.; Delves, L. M.
    J. Comput. Phys. 41 (1981), no. 2, 444--452, MathSciNet.  
  36. Exact Monte Carlo solution of elliptic partial differential equations.
    Booth, Thomas E.
    J. Comput. Phys. 39 (1981), no. 2, 396--404, MathSciNet.  
  37. On preconditioned iterative methods for elliptic partial differential equations.
    Evans, David J.
    Elliptic problem solvers (Santa Fe, N.M., 1980), pp. 261--269, Academic Press, New York-London, 1981, MathSciNet.  
  38. Projection methods for monotone elliptic partial differential equations.
    Baranger, J.; Dumont, T.
    Nonlinear problems of analysis in geometry and mechanics (Proc. Sympos., Univ. Paul Sabatier, Toulouse, 1979), pp. 86--92, Res. Notes in Math., 46, Pitman, Boston, Mass.-London, 1981, MathSciNet.  
  39. On the Observed Rate of Convergence of an Iterative Method Applied to a Model Elliptic Difference Equation  
    R. A. Nicolaides  
    Mathematics of Computation, Vol. 32, No. 141. (Jan., 1978), pp. 127-133, Jstor.
  40. High accuracy finite difference approximation to solutions of elliptic partial differential equations.    
    Lynch, Robert E.; Rice, John R.    
    Proc. Nat. Acad. Sci. U.S.A. 75 (1978), no. 6, 2541--2544, MathSciNet.   
  41. Numerical solution of nonlinear elliptic partial differential equations by a generalized conjugate gradient method.
    Concus, P.; Golub, G. H.; O'Leary, D. P.
    Computing 19 (1977/78), no. 4, 321--339, MathSciNet.  
  42. Mesh refinement and local inversion of elliptic partial differential equations.
    Hyman, James M.
    J. Computational Phys. 23 (1977), no. 2, 124--134, MathSciNet.  
  43. Orthogonal collocation for elliptic partial differential equations.
    Prenter, P. M.; Russell, R. D.
    SIAM J. Numer. Anal. 13 (1976), no. 6, 923--939, MathSciNet.  
  44. An optimum SOR procedure for the solution of elliptic partial differential equations with any domain or coefficient set.
    Brazier, P. H.
    Comput. Methods Appl. Mech. Engrg. 3 (1974), no. 3, 335--347, MathSciNet.  
  45. Quadrature-Galerkin Approximations to Solutions of Elliptic Differential Equations  
    Martin H. Schultz  
    Proceedings of the American Mathematical Society, Vol. 33, No. 2. (Jun., 1972), pp. 511-515, Jstor.
  46. Integral equation method for solution of boundary value problems of structural mechanics. II.
    Hajdin, Nikola; Krajcinovic, Dusan
    Elliptic partial differential equations. Internat. J. Numer. Methods Engrg. 4 (1972), 523--539, MathSciNet.  
  47. Periodicity Effects on the Iterative Solution of Elliptic Difference Equations  
    Winifred L. Wood  
    SIAM Journal on Numerical Analysis, Vol. 8, No. 2. (Jun., 1971), pp. 439-464, Jstor.
  48. Approximate Solution and Error Bounds for Quasi-Linear Elliptic Boundary Value Problems  
    J. B. Rosen  
    SIAM Journal on Numerical Analysis, Vol. 7, No. 1. (Mar., 1970), pp. 80-103, Jstor.
  49. Note on the Representation of a Solution of an Elliptic Differential Equation Near an Isolated Singularity  
    David G. Schaeffer  
    Proceedings of the American Mathematical Society, Vol. 23, No. 2. (Nov., 1969), pp. 450-454, Jstor.
  50. Numerical Analysis of an Elliptic-Parabolic Partial Differential Equation  
    Joel N. Franklin; Eugene R. Rodemich  
    SIAM Journal on Numerical Analysis, Vol. 5, No. 4. (Dec., 1968), pp. 680-716, Jstor.
  51. Difference methods for a nonlinear elliptic system of partial differential equations.    
    McAllister, G. T.    
    Quart. Appl. Math. 23 1965/1966 355--359, MathSciNet.   
  52. A New Technique for Solving Elliptic Partial Differential Equations  
    G. J. Tee  
    Journal of the Society for Industrial and Applied Mathematics, Vol. 12, No. 2. (Jun., 1964), pp. 311-347, Jstor.
  53. The application of relaxation methods to the solution of non-elliptic partial differential equations. III. Heat conduction, with change of state, in two space dimensions.
    Allen, D. N. de G.; Severn, R. T.
    Quart. J. Mech. Appl. Math. 15 1962 53--62, MathSciNet.  
  54. The numerical solution of elliptic and parabolic partial differential equations.
    Young, David
    1961 Modern mathematics for the engineer: Second series pp. 373--419 McGraw-Hill, New York, MathSciNet.  
  55. Iterative methods for the solution of elliptic partial differential equations.
    Sheldon, J. W.
    1960 Mathematical methods for digital computers pp. 144--156 Wiley, New York, MathSciNet.  
  56. Integration of the Laminar Boundary Layer Equation. I. Motion of an Elliptic Cylinder. Separation  
    D. Meksyn  
    Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, Vol. 201, No. 1065. (Mar. 22, 1950), pp. 268-278, Jstor.
  57. Kernel functions in the theory of partial differential equations of elliptic type.
    Bergman, S.; Schiffer, M.
    Duke Math. J. 15, (1948). 535--566, MathSciNet.  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2004