Refereed Publications

1. Russell, R.D. and Shampine, L.F., Existence of eigenvalues of integral equations. SIAM Review 13, 209-219 (1971).

2. Burgmeier, J.W., Russell, R.D., and Shampine, L.F., Integral equations with transform kernels and the eigenproblem KC v = v, Numer. Math. 17, 253-267 (1971).

3. Russell, R.D., and Shampine, L.F., A collocation method for boundary value problems (I and II). Num. Math. 19, 1-28 (1972).

4. Russell, R.D., and Shampine, L.F., Numerical methods for singular boundary value problems. SIAM J. Num. Anal. 12, 13-36 (1975).

5. Russell, R.D., Collocation for systems of boundary value problems. Num. Math 23, 4, 119-133 (1974).

6. Russell, R.D., and Varah, J.M., A comparison of global methods for two-point boundary value problems. Math. of Comp. 29, 1007-1019 (1975).

7. Prenter, P.M. and Russell, R.D., Collocation for elliptic partial differential equations. SIAM J. Numer. Anal.13, 923-939 (1976).

8. Russell, R.D., A comparison of collocation and finite differences for two-point boundary value problems. SIAM J. Numer. Anal. 14, No. 1, 19-39 (1977).

9. Russell, R.D., Efficiencies of B-spline methods for solving differential equations. 5th Manitoba Conference on Num. Math., 599-617 (1975).

10. Russell, R.D., and Christiansen, J., Adaptive mesh selection strategies for solving boundary value problems. SIAM J. Numer. Anal. 15, No. 1, 59-80 (1978).

11. Christiansen, J., and Russell, R.D., Error analysis for spline collocation methods with application to knot selection, Math. of Comp. 32, 415-419 (1978).

12. Ascher, U., Christiansen, J., and Russell, R.D., A collocation solver for mixed order systems of boundary value problems. Math. of Comp. 33, 659-679 (1979).

13. Ascher, U., Christiansen, J., and Russell, R.D., COLSYS - a collocation code for boundary value problems. Proceedings of Working Conference for Codes for Boundary Value Problems in ODE's, Springer-Verlag, Vol. 76, 164-185 (1979).

14. Russell, R.D., Mesh selection methods. Proceedings of Working Conference for Codes for Boundary Value Problems in ODE's, ibid., 228-242.

15. Ascher, U., Christiansen, J., and Russell, R.D., Collocation software for boundary value ODE's, ACM Trans. on Math. Software 7 209-222 (1981).

16. Ascher, U., Christiansen, J., and Russell, R.D., Algorithm COLYSYS: collocation software for boundary value ODE's, ACM Trans. on Math. Software 7, 223-229 + 40 page microfiche (1981).

17. Christiansen, J., and Russell, R.D., Deferred corrections using uncentered end formulas, Num. Math. 35, 21-33 (1980).

18. Russell, R.D., Global codes for BVODE's and their comparison, Numerical Integration of Differential Equations and Large Linear Systems, 256-268, Lecture Notes in Mathematics, Vol. 968, Springer-Verlag (1982).

19. Pereyra, V., and Russell, R.D., Solucion numerica de problemas de Frontera ordinarios mediante metodos globules. Proc. of VII Latin American Conference on Information Science, 420-425 (1980).

20. Ascher, U., and Russell, R.D., Reformulation of boundary value problems into "standard" form. SIAM Review 23, 238-254 (1981).

21. Russell, R.D., Difficulties in evaluating differential equation software, Numerical Analysis, pp. 175-184, Lecture Notes in Mathematics, Vol. 909, Springer-Verlag (1982).

22. Pereyra, V., and Russell, R.D., Difficulties of comparing complex mathematical software: General Comments and the BVODE case, Acta Cient. Venezolana, Vol. 33, 15-22 (1982).

23. Ascher, U., Pruess, S., and Russell, R.D., On spline basis selection for solving differential equations, SIAM J. Num. Anal. 20, 121-142 (1983).

24. Lentini, M., Osborne, M. and Russell, R.D., The close relationships between methods for solving two point boundary value problems. SIAM Journal of Numerical Analysis 22, 280-309 (1985).

25. Russell, R.D., A unified view of some recent developments in the numerical solution of BVODE's, pp 1-20 in Numerical Boundary Value ODE's (ed. U. Ascher and R.D. Russell) Progress in Scientific Computing Vol. 5, Birkhauser, 1985.

26. Paine, J., and Russell, R.D., Conditioning of collocation matrices and discrete Greens functions. SIAM J. Num. Anal. 23, 376-392 (1986)

27. Ascher, U., and R.D. Russell, Editors, Numerical Boundary Value ODE's, Progress in Scientific Computing, Vol. 5, Birkhauser (1985).

28. Osborne, M.R. and Russell, R.D., The Riccati transformation in the solution of boundary value problems. SIAM J. Numer. Anal. 23, 1023-1033 (1986).

29. L. Dieci and R.D.Russell, Riccati and other methods for singularly perturbed BVP, 27-38. Proc. of IVC International Conference of Boundary and Interior Layers - Computational and Asymptotic Methods. Boole Press (1986).

30. L. Dieci, M.R. Osborne and R.D. Russell, A Riccati transformation method for solving linear BVP's 1: theoretical aspects. SIAM J. Numer. Anal. 25, 1055-1073 (1988).

31. L. Dieci, M.R. Osborne and R.D. Russell, A Riccati transformation method for solving linear BVP's 1: computational aspects. SIAM J. Numer. Anal. 25, 1074-1092 (1988).

32. U. Ascher, R.M.M. Mattheij and R.D. Russell, Numerical Solution of Boundary Value Problems for Ordinary Differential Equations. Prentice-Hall (1988).

33. L. Dieci and R.D.Russell, Some Aspects of invariant subspaces computation, Procs. of the International Conference on Asymptotic and Computational Analysis, 565-585, R. Wong ed., M. Dekker (1989).

34. J.R.Cash, R.D. Russell, and Y. Ren, Boundary Value Problem Continuation with Moving Meshes, Proc. of Conference on Computational ODES, L. Gladwell et al., eds., Oxford Univ. Press (1991).

35. L. Dieci, J. Lorenz, and R.D. Russell, Numerical calculation on invariant tori, SIAM J. Sci. Stat. Comput. 12, 607-647 (1991).

36. S. Bramley, L. Dieci, and R.D. Russell, Numerical Solution of eigenvalue problems for linear boundary value ODEs, J. of Comp. Phys. 94, 382-402 (1991).

37. L. Liu and R.D. Russell, Boundary Value ODE algorithms for bifurcation analysis, Proc. of 13th IMACS World Congress on Comp. Appl. Math., Bail Press (1991), 302-303.

38. R.D. Russell, D.M. Sloan, M.R. Trummer, On the structure of Jacobians for spectral methods for nonlinear PDE's, SIAM J. Sci. Stat. Comp., 13 (1992), 541-549.

39. R.D. Russell, D.M. Sloan, M.R. Trummer, Some numerical aspects of computing inertial manifolds, SIAM J. Sci. Comp. 14 (1993), 19-43.

40. Y. Ren and R.D. Russell, Moving mesh techniques based upon equidistribution and their stability, SIAM J. Sci. Stat. Comp. 13 (1992), 1265-1286.

41. L. Liu and R.D. Russell, Linear System solvers for boundary value ODEs, Journal of Comp. Appl. Maths, 45 (1993), 103-117.

42. Y. Ren and R.D. Russell, On moving mesh methods for solving time dependent PDEs, in Numerical Methods in Engineering and Applied Science, CIMNE, Barcelona (1992), 76-85.

43. J.R. Cash, R.D. Russell, and Y. Ren, Boundary value problem continuation with moving meshes, in Computational Ordinary Differential Equations, Oxford Univ. Press (1992), 201-214.

44. K. Edoh and R.D. Russell, Numerical Approximation of invariant circles, in Compuational ODEs, University Press, PLC, Ibadan, 1992, 36-45.

45. L. Dieci, R.D. Russell, and E.S. Van Vleck, Unitary integrators and applications to continuous orthonomalization techniques, SIAM J. Numer. Anal., 31 (1994), 261-281.

46. W. Huang, Y. Ren and R.D. Russell, Moving mesh partial differential equations based on the equidistribution principle, SIAM J. Numer. Anal. 31 (1994), 709-730.

47. W. Huang, Y. Ren, and R.D. Russell, Moving mesh methods based on moving mesh partial differential equations, J. Comp. Phys. 113, (1994), 279-290.

48. J. Butcher, J. Cash, G. Moore and R.D. Russell, Defect correction for two-point boundary value problems on nonequidistant meshes, Math. Comp. 64 (1995), 629-648.

49. W. Huang and R.D. Russell, Moving mesh strategies for solving partial differential equations, in Proc. of 14th IMACS World Congress on Comp. and Applied Mathematics (1994), 1315-1318.

50. C.J. Budd, W. Huang, and R.D. Russell, Moving mesh methods for problems with blow-up, SIAM J. Sci. Comput. 17 (1996), 305-327.

51. W. Sun, W. Huang, and R.D. Russell, Finite Difference Preconditioning for Solving Orthogonal Collocation Equations for Boundary Value Problems, SIAM J. Numer. Anal. 33 (1996), 2268-2285.

52. L. Dieci, R.D. Russell, and E.S. Van Vleck, On the Computation of Lyapunov Exponents for Continuous Dynamical Systems, SIAM J. Numer. Anal. 34 (1997), 402-423.

53. W. Huang and R.D. Russell, Analysis of Moving Mesh Partial Differential Equations with Spatial Smoothing, SIAM J. Numer. Anal. 34 (1997), 1106-1126.

54. R.D. Russell and W. Sun, Spline Collocation Differentiation Matrices, SIAM J. Numer. Anal. 34 (1997), 2274-2287.

55. W. Huang and R.D. Russell, A Moving Collocation Method for the Numerical Solution of Time Dependent Partial Differential Equations, Appl. Num. Math. 20 (1996), 101-116.

56. L. Liu, G. Moore, and R.D. Russell, Computation and Continuation of homoclinic and Heteroclinic Orbits with Arclength Parameterization, SIAM J. Sci. Comput. 18 (1997), 69-94.

57. D. H. Hepting, G. Derks, K. D. Edoh, and R.D. Russell, Qualtitative Analysis of Invariant Tori in a Dynamical System, VISUALIZATION '95 Proceedings, edited by G. M. Nielson and D. Silver, IEEE Computer Society Press, 1995.

58. C. J. Budd, J. Chen, W. Huang and R.D. Russell, Moving Mesh Methods with Applications to Blow-up Problems for PDEs, Numerical Analysis 1995: Proc. of 1995 Biennial Conference on Numerical Analysis, Ed. by D. F. Griffiths and G. A. Watson, Pitman Research Notes in Mathematics, Longman Scientific and Technical (1996), 1-17.

59. W. Huang and R.D. Russell, Moving Mesh Strategy Based upon a Gradient Flow Equation for Two Dimensional Problems, SIAM J. Sci. Comput. 20 (1999), 998-1015.

60. W. Huang and R.D. Russell, A High Dimensional Moving Mesh Strategy, Appl. Num. Math. 26 (1997), 63-76.

61. W. Cao, W. Huang and R. D. Russell, A Study of Monitor Functions for Two Dimensional Adaptive Mesh Generation, SIAM J. Sci. Comput., 20 (1999), 1978-1994.

62. C. Budd, G. Collins, W. Huang and R. D. Russell, Self-similar Numerical Solutions of the Porous Medium Equation Using Moving Mesh Methods, Phil Trans. Roy. Soc. 357 (1999), 1047-1078.

63. W. Cao, W. Huang and R. D. Russell, An $r$-Adaptive Finite Element Method Based upon Moving Mesh PDEs, J. Comp. Phys. 149 (1999), 221-244.

64. W. Cao, W. Huang and R. D. Russell, A Moving Mesh Method in Multi-Block Domains with Application to a Combustion Problem, Numerical Methods for Partial Differential Equations, 15 (1999), 449-467.

65. C. Budd, S. Chen and R. D. Russell, New Self-Similar Solutions of the Nonlinear Schrodinger Equation with Moving Mesh Methods, J. Comp. Phys. 152 (1999), 756-789.

66. K. D. Edoh, R. D. Russell and W. Sun, Computation of Invariant Tori by Orthogonal Collocation, Appl. Num. Math. 32 (2000), 273-289.

67. W. Huang and R.D. Russell, Adaptive Mesh Movement -- the MMPDE Approach and its Applications, J. Comp. Appl. Math. 128 (2001), 383-398.

68. J. Stockie, J. Mackenzie and R.D. Russell, A Moving Mesh Method for One-dimensional Hyperbolic Conservation Laws, SIAM J. Sci. Comput. 22 (2001), 1791-1813.

69. W. Cao, W. Huang and R. D. Russell, Comparison of Two-Dimensional $r$-Adaptive Finite Element Methods Using Various Error Indicators, J. Math. and Computers in Simulation, 56 (2001), 127--143.

70. W. Cao, W. Huang and R. D. Russell, An Error Indicator Monitor Function for an $r$-Adaptive Finite Element Method, J. Comp. Phys. 170 (2001), 871-892.

71. W. Cao, W. Huang and R. D. Russell, A Moving Mesh Method Based on the Geometric Conservation Law, SIAM J. Sci. Comput., 24 (2003), 118-142.

72. C. J. Budd, H. Huang and R. D. Russell, Mesh Selection for a Nearly Singular Boundary Value Problem, J. Sci. Comput. 16 (2002), 525-552.

73. W. Cao, R. Carretero-Gonzalez, W. Huang and R. D. Russell, Variational mesh adaptation methods for axisymmetrical domains, SIAM J. Numer. Anal. 41 (2003), 235-257.

74. J. Lang, W. Cao, H. Huang and R. D. Russell, A two-dimensional moving finite element method with local refinement based on a posteriori error estimates, Appl. Num. Math., 46 (2003), 75-94.

75. W. Cao, W. Huang and R. D. Russell, Approaches for Generating Moving Adaptive Meshes: Location versus Velocity, Appl. Num. Math., 47 (2003), 121-138.

76. S. Chen, R. D. Russell and W. Sun, Comparison of Some Moving Mesh Methods in Higher Dimensions, Advances on Scientific Computing and Applications, Science Press, Beijing/New York, pp. 117-132 (2004).

77. C. J. Budd, R. Carretero-Gonzalez and R. D. Russell, Precise computations of chemotactic collapse using moving mesh methods, J. Comp. Phys. 202 (2005), 463-487.

78. W. Sun, M. J. Ward and R. D. Russell, The Slow Dynamics of Two-spike Solutions for the Gray-Scott and Gierer-Meinhardt Systems: Competition and Oscillatory Instabilities, SIAM J. Appl. Dyn. Systems 4 (2005), 904-953.

79. P. Sun, R. D. Russell and J. Xu, A New Adaptive Local Mesh Refinement Algorithm and its Application on Fourth Order Thin Film Flow Problem, J. Comp. Phys. 224 (2007), 1021-1048.

80. R. D. Russell, J. F. Williams, and X. Xu, MOVCOL4: A Moving Mesh Code for Fourth-Order Time-Dependent Partial Differential Equations, SIAM J. Sci. Comput., 29 (2008), 197-220.

81. R. D. Russell, J. F. Williams, and X. Xu, A Comparison of Direct Discretization of Fourth-Order Problems Versus System Reduction, Proceedings of Shanghai Forum on Industrial and Applied Mathematics, Series in Comtemporary Applied Mathematics, ed. Ph.Ciarlet and Li Da-qian, World Scientific Press, pp. 195-205 (2007).

82. R. D. Haynes and R. D. Russell, A Schwarz Waveform Moving Mesh Method, SIAM J. Sci. Comput. 29 (2008), 656-673.

83. R. D. Haynes, W. Huang and R. D. Russell, A Moving Mesh Method for Time--dependent Problems based on Schwarz Waveform Relaxation, Proceedings of the 17th International Domain Decomposition Methods Meeting, Lecture Notes in Computational Science and Engineering (LNCSE) Vol. 60, Springer--Verlag, 229--236 (2008).

84. W. Huang, J. Ma, and R. D. Russell, A Study of Moving Mesh PDE Methods for Numerical Simulation of Blowup in Reaction Diffusion Equations, J. Comp. Phys. 227 (2008), 6532-6552.

85. T. Moeller, B. Hamann, and R. D. Russell, Mathematical Foundations of Scientific Visualization, Computer Graphics, and Massive Data Exploration. Springer Verlag series in Mathematics and Visualization, 2009.

86. C. J. Budd, W. Huang, and R. D. Russell, Adaptivity with moving grids, Acta Numerica, Volume 18, May 2009, pp 111-241.

87. M. Sulman, J. F. Williams, and R. D. Russell, Monge Kantorovich Approach for Grid Generation, Proceedings of International Conference of Numerical Analysis and Applied Mathematics, American Institute of Physics Conf. Proc., 1168 25-28 (2009).

88. X. Xu, W. Huang, R. D. Russell, and J. F. Williams, Convergence of De Boor's Algorithm for Generation of Equidistributing Meshes, IMA J. of Numer. Anal, 31 558-596 (2011).

89. M. Sulman, J. F. WIlliams, and R. D. Russell, An Efficient Approach for the Numerical Solution of the Monge-Ampere Equation, Appl. Numer. Math, 61 298-307 (2011).

90. M.H. Sulman, J. F. Williams, R.D. Russell, F.M. Beg, Volumetric image registration methods based on solving the Monge Ampere equation, Canadian Applied Mathematics Quarterly (Special Edition to Celebrate the 30th Anniversary of the Canadian Applied and Industrial Mathematics Society), to appear.

91. W. Huang and R. D. Russell, Adaptive Moving Mesh Methods, Series in Applied Mathematical Sciences, Springer, 2011.

92. M. Sulman, J. F. Williams, and R. D. Russell, Optimal Mass Transport for Higher Dimensional Adaptive Grid Generation, J. Comp. Phys. 230 3302-3330 (2011).

93. J. Ma, W. Huang, and R. D. Russell, Analysis of a Moving Collocation Method for One-Dimensional Partial Differential Equations, Science China Mathematics, 55 827-840 (2012).

94. Benjamin Ong, Robert Russell and Steven Ruuth, An h-r moving mesh method for one dimensional time-dependent PDEs, Proceedings of the 21st International Meshing Roundtable, Computational Intelligence and Complexity, Springer, 39--54 (2012).

95. C. J. Budd, R. D. Russell, and E. Walsh, The Geometry of r-Adaptive Meshes Generated Using Optimal Transport Methods, J. Comp. Phys., Vol. 282, 113--137 (2015).

96. Weizhang Huang, Lennard Kamenski, and Robert D. Russell, A Comparative Numerical Study of Meshing Functionals for Variational Mesh Adaptation, J. Math. Study, Vol. 48, 168--186 (2015).

97. Benjamin Crestel, Robert D. Russell, and Steven J. Ruuth, Moving mesh methods on parametric surfaces, Proceedings of the International Meshing Roundtable, Austin, 148--160 (2015).

98. Robert D. Russell, Adaptive Mesh Refinement, Encyclopedia of Applied and Computational Mathematics, Springer, 23--25 (2015).