Difference schemes of optimal type for an approximate solution of parabolic equations (Banach case). (English. Russian original) Zbl 0484.65033
Ukr. Math. J. 33, 30-36 (1981); translation from Ukr. Mat. Zh. 33, 39-46 (1981).
MSC:
| 65J10 | Numerical solutions to equations with linear operators |
| 35G10 | Initial value problems for linear higher-order PDEs |
| 35K25 | Higher-order parabolic equations |
| 34G10 | Linear differential equations in abstract spaces |
| 65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |
| 65M12 | Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs |
| 65K10 | Numerical optimization and variational techniques |
Keywords:
two-level difference schemes; Cauchy-Dirichlet problem; Banach space; optimal type; Pade fraction; bilateral asymptotic estimatesReferences:
| [1] | P. E. Sobolevskii and Khoang Van Lai, ?Difference schemes of optimal type for approximating solutions of parabolic equations,? Ukr. Mat. Zh.,32, No. 5, 623-629 (1980). |
| [2] | Kh. A. Alibekov and P. E. Sobolevskii, ?Stability of difference schemes of higher order for parabolic equations,? Dokl. Akad. Nauk SSSR,232, No. 4, 737-740 (1977). |
| [3] | P. E. Sobolevskii, ?Theory of semigroups and stability of difference schemes,? Preprint, VTs Sib. Otd. Akad. Nauk SSSR (1975). |
| [4] | M. A. Krasnosel’skii et al., Integral Operators in Spaces of Summable Functions [in Russian], Nauka, Moscow (1966). |
| [5] | W. B. Saff and R. S. Varga, ?On the zeros and poles of Pade approximants to ez,? Numer. Math.,25, No. 1, 1-14 (1975). · Zbl 0322.41010 · doi:10.1007/BF01419524 |
| [6] | T. Kato, Perturbation Theory for Linear Operators, Springer-Verlag (1966). · Zbl 0148.12601 |
| [7] | W. B. Graff, ?The Pade table and its relation to certain algorithms of numerical analysis,? SIAM Rev.,14, No. 1, 1-62 (1972). · Zbl 0238.30008 · doi:10.1137/1014001 |
| [8] | S. P. Norsett, ?C-polynomials for rational approximation to the exponential function,? Numer. Math.,25, No. 1, 39-56 (1975). · Zbl 0299.65010 · doi:10.1007/BF01419527 |
| [9] | N. I. Akhiezer, Theory of Approximation, Ungar (1956). · Zbl 0072.43701 |
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