Rothe's method for the heat equation and boundary integral equations

Journal of Integral Equations and Applications

Volumn 9, Issue 1, 1997, Pages 47-69

  Chapko, Roman ^a   Kress, Rainer ^b  

^a IVAN FRANKO NATIONAL UNIVERSITY OF LVIV   (Ukraine)

^b UNIVERSITY OF GÖTTINGEN   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0002642482     PISSN: 08973962     EISSN: None     Source Type: Journal    
DOI: 10.1216/jiea/1181075987     Document Type: Article

References (23)

1. D.N. Arnold and D.N. Noon, Coercitivity of the single layer heat potential, J. Comput. Math. 7 (1989), 100-104.
2. C.A. Brebbia, J.C. Telles and L.C. Wrobel, Boundary element techniques, Springer-Verlag, New York, 1984.
3. R. Chapko and R. Kress, On a quadrature method for a logarithmic integral equation of the first kind, in Contributions in numerical mathematics (Agarwal, ed.), World Scientific, Singapore, 1993.
4. R. Chapko, On the numerical solution of initial boundary value problems by the Laguerre transformation and boundary integral equations, in Proceedings of the second Japan-Novosibirsk joint seminar on inverse and ill-posed problems, Iso and Yamamoto, eds., to appear.
5. D. Colton and R. Kress, Inverse acoustic and electromagnetic scattering theory, Springer-Verlag, Berlin, 1992.
6. M. Costabel, Boundary integral operators for the heat equation, Integral Equations Operator Theory 13 (1990), 498-552.
7. A Friedman, Partial differential equations of parabolic type, Prentice-Hall, Englewood Cliffs, 1964
8. W. Galazjuk and R. Chapko, The Chebyshev-Laguerre transformation and integral equations for exterior boundary value problems for the telegraph equation, Dokl. Akad. Nauk. UzSSR 8 (1990), 11-14 (in Russian).
9. 3, mit einer Integralgleichungsmethode nach dem Rothe- verfahren, Computing 19 (1978), 251-268.
10. M. Gevrey, Sur les équations aux derivees partielles du type parabolique, J. de Math. 9 (1913), 305-471.
11. E. Holmgren, Sur l'équation de la propagation de la chaleur, Arkiv Mat. Fysik. 4 (1908), 1-11.
12. E. Holmgren, Sur l'équation de la propagation de la chaleur II, Arkiv Mat. Fysik. 4 (1908), 1-28.
13. G.C. Hsiao and J. Saranen, Boundary integral solution of the two-dimensional heat equation, Math. Methods Appl. Sci. 16 (1993), 87-114.
14. R. Kress, Linear integral equations, Springer-Verlag, New York, 1989.
15. R. Kress and I.H. Sloan, On the numerical solution of a logarithmic integral equation of the first kind for the Helmholtz equation, Numer. Math. 66 (1993), 199-214.
16. N.N. Lebedev, Special functions and their applications, Prentice-Hall, Engle wood Cliffs, 1965.
17. C. Lubich and R. Schneider, Time discretizations of parabolic boundary integral equations, Numer. Math. 63 (1992), 455-481.
18. C. Lubich, On the multistep time discretizations of linear initial-boundary value problems and their boundary integral equations, Numer. Math. 67 (1994), 365-390.
19. E. Martensen, The Rothe method for the wave equation in several space dimensions, Proc. Royal Soc. Edinburgh, Sect. A 84 (1979), 101-113.
20. C.H. Müntz, Zum dynamischen Warmeleitungsproblem, Math. Z. 38 (1934), 323-337.
21. M.H. Protter and H.F. Weinberger, Maximum principles in differential equations, Prentice-Hall, Englewood Cliffs, 1967.
22. K. Rektorys, The method of discretization in time, D. Reidel Publishing Company, Dordrecht, 1982.
23. E. Rothe, Zweidimensionale parabolische Randwertaufgaben als Grenzfall eindimensionaler Randwertaufgaben, Math. Anal. 102 (1930), 650-670