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Collocation methods for linear elliptic problems. (English) Zbl 0397.65076


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
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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
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