Domain decomposition methods for pseudo spectral approximations. I. Second order equations in one dimension. (English) Zbl 0637.65077

Multidomain pseudo spectral approximations of second order Neumann- Dirichlet boundary value problems in one dimension are considered. The equation is collocated at the Chebyshev nodes inside each in subinterval. Different parching conditions at the interfaces are analyzed. Some numerical experiments are discussed.
Reviewer: K.Najzar


65L10 Numerical solution of boundary value problems involving ordinary differential equations
65L20 Stability and convergence of numerical methods for ordinary differential equations
34B05 Linear boundary value problems for ordinary differential equations
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[1] Canuto, C., Quarteroni, A.: Spectral and pseudo-spectral methods for parabolic problems with non periodic boundary conditions. Calcolo18, 197-217 (1981) · Zbl 0485.65078 · doi:10.1007/BF02576357
[2] Canuto, C., Quarteroni, A.: Approximation results for orthogonal polynomials in Sobolev spaces. Math. Comput.38, 67-86 (1982) · Zbl 0567.41008 · doi:10.1090/S0025-5718-1982-0637287-3
[3] Canuto, C., Quarteroni, A.: Error estimates for spectral and pseudo-spectral approximation of hyperbolic equations. SIAM J. Numer. Anal.19, 629-642 (1982) · Zbl 0508.65054 · doi:10.1137/0719044
[4] Canuto, C., Quarteroni, A.: Variational methods in the theoretical analysis of spectral approximation. In: Spectral methods for Partial Differential Equations (R. Voigt, D. Gottlieb, Y. Hussaini, eds.), pp. 55-78, Philadelphia, SIAM 1984 · Zbl 0539.65080
[5] Davis, P.J., Rabinowitz, P.: Methods of Numerical Integration. New York: Academic Press 1975 · Zbl 0304.65016
[6] Funaro, D.: A multidomain spectral approximation of elliptic equations. Numerical Methods for P.D.E.2, 187-205 (1986) · Zbl 0622.65104 · doi:10.1002/num.1690020304
[7] Orszag, S.A.: Spectral methods for problems in complex geometries. J. Comput. Phys.37, 70-92 (1980) · Zbl 0476.65078 · doi:10.1016/0021-9991(80)90005-4
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