Orthogonal spline collocation methods for partial differential equations

Journal of Computational and Applied Mathematics

Volumn 128, Issue 1-2, 2001, Pages 55-82

  Bialecki, B ^a   Fairweather, G ^a  

^a Department of Metallurgical and Materials Engineering   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY VALUE PROBLEMS;

GAUSS POINTS;

DIFFERENTIAL EQUATIONS;

DIFFERENTIAL EQUATION;

EID: 0035281751     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0377-0427(00)00509-4     Document Type: Article

References (143)

1. Orthogonal spline collocation for quasilinear elliptic Dirichlet boundary value problems
2. Almost block diagonal linear systems: Sequential and parallel solution techniques, and applications
3. 4) cubic spline collocation method for quasilinear parabolic equations
4. Alternating direction collocation methods for simulating reservoir performance
5. An alternating direction implicit method for orthogonal spline collocation linear systems
6. A fast domain decomposition Poisson solver on a rectangle for Hermite bicubic orthogonal spline collocation
7. Cyclic reduction and FACR methods for piecewise Hermite bicubic orthogonal spline collocation
8. Preconditioned Richardson and minimal residual iterative methods for piecewise Hermite bicubic orthogonal spline collocation equations
9. Convergence analysis of orthogonal spline collocation for elliptic boundary value problems
10. Superconvergence of orthogonal spline collocation in the solution of Poisson's equation
11. 1-norm error estimates for piecewise Hermite bicubic orthogonal spline collocation schemes for elliptic boundary value problems
12. An additive Schwarz algorithm for piecewise Hermite bicubic orthogonal spline collocation
13. Fourier analysis of Schwarz alternating methods for piecewise Hermite bicubic orthogonal spline collocation
14. Multilevel additive and multiplicative methods for orthogonal spline collocation problems
15. Matrix decomposition algorithms for separable elliptic boundary value problems in two dimensions
16. Matrix decomposition algorithms in orthogonal spline collocation for separable elliptic boundary value problems
17. Fast direct solvers for piecewise Hermite bicubic orthogonal spline collocation equations
18. Fourier methods for piecewise Hermite bicubic orthogonal spline collocation
19. Orthogonal spline collocation Laplace-modified and alternating-direction collocation methods for parabolic problems on rectangles
20. An orthogonal spline collocation alternating direction implicit Crank-Nicolson method for linear parabolic problems on rectangles
21. Fourier matrix decomposition method for least squares solution of singular neumann and periodic hermite bicubic collocation problems
22. Fast numerical solution of the biharmonic dirichlet problem on rectangles
23. Collocation at Gauss points
24. The alternating direction collocation approximation
25. The basis spline method and associated techniques
26. Spline methods for conservation equations
27. Orthogonal collocation and alternating-direction methods for unsaturated flow
28. Collocation solution of the transport equations using a locally enhanced alternating direction formulation
29. An analysis of alternating-direction methods for parabolic equations
30. Generalized alternating-direction collocation methods for parabolic equations. I. Spatially varying coefficients
31. Generalized alternating-direction collocation methods for parabolic equations. II. Transport equations with application to seawater intrusion problems
32. Generalized alternating-direction collocation methods for parabolic equations. III. Nonrectangular domains
33. Alternating-direction collocation solution to the transport equation
34. Collocation methods for parabolic partial differential equations in one space dimension
35. Schur complement preconditioned conjugate gradient methods for spline collocation equations
36. Quadratic spline collocation methods for elliptic partial differential equations
37. Parallel solvers for spline collocation equations
38. Multigrid and multilevel methods for quadratic spline collocation
39. A mixed finite element method for the biharmonic equation
40. Fast fourier transform solvers for quadratic spline collocation
41. Domain-embedding alternating direction method for linear elliptic equations on irregular regions using collocation
42. Alternating direction collocation for irregular regions
43. A coupled double splitting ADI scheme for first biharmonic using collocation
44. Alternating direction collocation for separable elliptic partial differential equations
45. Parallel computing for solute transport models via alternating direction collocation
46. Extrapolated collocation for two-point boundary value problems using cubic splines
47. FORTRAN packages for solving certain almost block diagonal linear systems by modified alternate row and column elimination
48. Algorithm 603 COLROW and ARCECO: FORTRAN packages for solving certain almost block diagonal linear systems by modified alternate row and column elimination
49. A superconvergence result for the approximate solution of the heat equation by a collocation method
50. Alternating direction Galerkin methods on rectangles
51. A finite element collocation method for the heat equation
52. A finite element collocation method for quasilinear parabolic equations
53. Tensor product generalized ADI methods for separable elliptic problems
54. A tensor product generalized ADI method for the method of planes
55. Computation of invariant tori by orthogonal collocation
56. Spline collocation methods for a class of hyperbolic partial integro-differential equations
57. Parallel matrix decomposition algorithms for separable elliptic boundary value problems
58. Matrix decomposition algorithms for modified cubic spline collocation for separable elliptic boundary value problems. I. Helmholtz problems
59. A survey of spline collocation methods for the numerical solution of differential equations
60. Efficient orthogonal spline collocation methods for solving linear second order hyperbolic problems on rectangles
61. Analysis of alternating direction collocation methods for parabolic and hyperbolic problems in two space variables
62. The collocation method for the quasi-linear elliptic equation of second order
63. The collocation method for a quasi-linear parabolic equation in two space variables
64. Analyses of spline collocation methods form parabolic and hyperbolic problems in two space variables
65. Iterative line cubic spline collocation methods for elliptic partial differential equations in several dimensions
66. Analysis of iterative line spline collocation methods for elliptic partial differential equations
67. Modified successive overrelaxation (MSOR) and equivalent 2-step iterative methods for collocation matrices
68. An alternating-direction collocation method for finite element approximation on rectangles
69. A comparison of alternating-direction collocation methods for the transport equation
70. Alternating-direction collocation for rectangular regions
71. Application of method of collocation on lines for solving nonlinear hyperbolic problems
72. Collocation methods for linear elliptic problems
73. Quadratic-spline collocation methods for two-point boundary value problems
74. Collocation software for second-order elliptic partial differential equations
75. Algorithm GENCOL: Collocation on general domains with bicubic hermite polynomials
76. Algorithms INTCOL and HERMCOL: Collocation on rectangular domains with bicubic hermite polynomials
77. Parallelization of a new class of cubic spline collocation methods
78. 4) cubic spline collocation methods for elliptic partial differential equations
79. 6) quintic spline collocation method for fourth order two-point boundary value problems
80. Algorithm 688: EPDCOL: A more efficient PDECOL code
81. Basis spline collocation method for solving the Schrödinger equation in axillary symmetric systems
82. Approximate methods for nonlinear problems with application to two-point boundary value problems
83. Finite difference preconditioning cubic spline collocation method of elliptic equations
84. Estimating convergence factors of Schwarz algorithms for orthogonal spline collocation method
85. 1 finite element method on an irregular mesh
86. Preconditioning cubic spline collocation discretizations of elliptic equations
87. A generalized Schwarz splitting method based on hermite collocation for elliptic boundary value problems
88. General interior Hermite collocation methods for second order elliptic partial differential equations
89. On the iterative solution of Hermite collocation equations
90. Numerical solution of linear elasticity by preconditioning cubic spline collocation
91. Discrete-time orthogonal spline collocation methods for Schrödinger equations in two space variables
92. A Crank-Nicolson orthogonal spline collocation method for vibration problems
93. Discrete-time orthogonal spline collocation methods for vibration problems
94. Orthogonal spline collocation methods for biharmonic problems
95. Algorithm 540. PDECOL: General collocation software for partial differential equations
96. Packages for solving almost block diagonal linear systems arising in spline collocation at Gaussian points with monomial basis functions
97. The solution of almost block diagonal linear systems arising in spline collocation at Gaussian points with monomial basis functions
98. Algorithm 704: ABDPACK and ABBPACK - FORTRAN programs for the solution of almost block diagonal linear systems arising in spline collocation at Gaussian points with monomial basis functions
99. Second-order splitting combined with orthogonal cubic spline collocation method for the Kuramoto-Sivashinsky equations
100. A second-order splitting combined with orthogonal cubic spline collocation method for the Rosenau equation
101. Numerical solution of an evolution equation with a positive type memory term
102. An experimental performance analysis of the rate of convergence of collocation on general domains
103. A method of lines package, based on monomial spline collocation, for systems of one-dimensional parabolic differential equations
104. 1 finite element collocation method for elliptic equations
105. Tensorial basis spline collocation method for poisson's equation
106. Fast three-dimensional elliptic solvers on distributed network clusters
107. Orthogonal collocation for elliptic partial differential equations
108. Orthogonal spline collocation solution of nonlinear Schrödinger equations, mathematics of computation 1943-1993: A half-century of computational mathematics, Vancouver, BC, 1993
109. The solution of nonlinear Schrödinger equations using orthogonal spline collocation
110. Orthogonal cubic spline collocation solution of underwater acoustic wave propagation problems
111. An orthogonal spline collocation method for the numerical solution of underwater acoustic wave propagation problems
112. Orthogonal spline collocation methods for Schrödinger-type equations in one space variable
113. Spline collocation differentiation matrices
114. Multigrid methods for computational acoustics on vector and parallel computers
115. Orthogonal collocation solution of biharmonic equations
116. Iterative algorithms for solving hermite bicubic collocation equations
117. A higher order direct method for solving poisson's equation on a disc
118. Block iterative algorithms for solving hermite bicubic collocation equations
119. Fast algorithms for high-order spline collocation systems
120. Spectral analysis of hermite cubic spline collocation systems
121. Finite difference preconditioning for solving orthogonal collocation for boundary value problems
122. A fast algorithm for solving the tensor product collocation equations
123. The direct solution of the discrete poisson equation on a disk
124. ADI methods for cubic spline collocation discretizations of elliptic PDEs
125. Three-dimensional HF and TDHF calculations with the basis-spline collocation technique
126. Basis-spline collocation method for the lattice solution of boundary value problems
127. Orthogonal spline collocation methods for some partial integrodifferential equations
128. Finite element methods for parabolic and hyperbolic partial integro-differential equations