Houstis, E. N. Collocation methods for linear elliptic problems. (English) Zbl 0397.65076 BIT, Nord. Tidskr. Inf.-behandl. 18, 301-310 (1978). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 6 Documents MSC: 65N35 Spectral, collocation and related methods for boundary value problems involving PDEs 35J25 Boundary value problems for second-order elliptic equations 65D07 Numerical computation using splines 65N40 Method of lines for boundary value problems involving PDEs 41A15 Spline approximation Keywords:Dirichlet and Neumann Boundary Conditions; a Priori Estimates; Numerical Results; Collocation Methods; Partial Differential Equations; Optimal Order; Hermite Cubic Polynomials; Splines; Linear Elliptic Problems PDFBibTeX XMLCite \textit{E. N. Houstis}, BIT, Nord. Tidskr. Inf.-behandl. 18, 301--310 (1978; Zbl 0397.65076) Full Text: DOI References: [1] J. C. Cavendish,Collocation Methods for Elliptic and Parabolic Boundary Value Problems, Ph.D. Thesis, University of Pittsburgh, 1972. [2] C. de Boor and B. Swartz,Collocation at Gaussian points, SIAM J. Numer. Anal. 10 (1973), 582–606. · Zbl 0232.65065 · doi:10.1137/0710052 [3] R. Dennemeyer,Introduction to partial differential equations and boundary value problems, McGraw-Hill, 1968. · Zbl 0156.10204 [4] E. N. Houstis,A collocation method for systems of nonlinear ordinary differential equations, Journal of Mathematical Analysis Applications 62 (1978), 24–37. · Zbl 0398.65052 · doi:10.1016/0022-247X(78)90215-9 [5] E. N. Houstis, R. E. Lynch, T. S. Papatheodorou, and J. R. Rice,Development, evaluation and selection of methods for elliptic partial differential equations, Ann. Assoc. Inter. Calcul. Analog. 11 (1975), 98–103. · Zbl 0302.65075 [6] E. N. Houstis, R. E. Lynch, T. S. Papatheodorou, and J. R. Rice,Evaluation of numerical methods for elliptic partial differential equations, Journal of Computational Physics 27 (1978). · Zbl 0381.65059 [7] F. Ito,A collocation method for boundary value problems using spline functions, Ph.D. Thesis, Brown University, 1972. [8] P. M. Prenter and R. D. Russell,Orthogonal collocation for elliptic partial differential equations, SIAM J. Numer. Anal. 13 (1976), 923–939. · Zbl 0366.65052 · doi:10.1137/0713073 [9] Yu. P. Yartsev,Convergence of the collocation method on lines, Diff. Uravneniya 3 (1967), 1606–1613. [10] Yu. P. Yartsev,The method of line collocation, Diff. Uravneniya 4 (1968), 925–931. [11] Yu. P. Yartsev,A variant of the line-collocation method, Diff. Uravneniya 6 (1970), 1727–1731. [12] R. S. Lehman,Developments at an analytic corner of solutions of partial differential equations, J. Math. Mech. 8 (1959), 727–760. · Zbl 0094.29702 [13] N. Wigley,Asymptotic expansions at a corner of solutions of mixed boundary value problems, J. Math. Mech. 13 (1964), 549–576. · Zbl 0178.45902 [14] E. N. Houstis,The complexity of numerical methods for elliptic partial differential equations, Journal of computational and applied mathematics (to appear). · Zbl 0383.65062 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.