Abstract
We study some discrete boundary value problems which are treated as digital approximation for starting boundary value problem for elliptic pseudo-differential equation. Starting from existence and uniqueness theorem we give a comparison between discrete and continuous solutions for certain boundary value problems.
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References
Eskin, G.I.: Boundary value problems for elliptic pseudodifferential equations. AMS Providence (1981)
Taylor, M.E.: Pseudo-Differential Operators. Princeton Univ. Press Princeton (1980)
Treves, F.: Introduction to Pseudodifferential Operators and Fourier Integral Operators. Springer New York (1980)
Samarskii, A.A.: The Theory of Difference Schemes. CRC Press Boca Raton (2001)
Ryaben’kii, V.S.: Method of Difference Potentials and its Applications. Springer-Verlag Berlin–Heidelberg (2002)
Vasilyev, A.V., Vasilyev, V.B.: Periodic Riemann problem and discrete convolution equations. Differ. Equ. 51, 652–660 (2015)
Vasilyev, A.V., Vasilyev, V.B.: Pseudo-differential operators and equations in a discrete half-space. Math. Model. Anal. 23 492–506 (2018)
Vasilyev, A.V., Vasilyev, V.B.: On some discrete boundary value problems in canonical domains. In: Differential and Difference Equations and Applications. Springer Proc. Math. Stat. V. 230, pp.569–579, Cham: Springer (2018)
Vasilyev, A.V., Vasilyev, V.B.: On some discrete potential like operators. Tatra Mt. Math. Publ. 71 195–212 (2018)
Vasilyev, A.V., Vasilyev, V.B.: On a digital approximation for pseudo-differential operators. Proc. Appl. Math. Mech. 17 763–764 (2017)
Vasilyev, V.B.: Discreteness, periodicity, holomorphy and factorization. In: Constanda, C., Dalla Riva, M., Lamberti, P.D., Musolino, P. (eds.) Integral Methods in Science and Engineering. V.1, pp. 315–324. Theoretical Technique. Springer, Cham. (2017)
Vasilyev, A., Vasilyev, V.: Digital Operators, Discrete Equations and Error Estimates. In: Radu, F., Kumar, K., Berre, I., Nordbotten, J., Pop, I. (eds.) Numerical Mathematics and Advanced Applications ENUMATH 2017. Lecture Notes in Computational Science and Engineering, vol 126, pp. 983–991. Springer, Cham. (2019)
Vasilyev, V.B.: Digital Approximations for Pseudo-Differential Equations and Error Estimates. In: Nikolov, G., Kolkovska, N., Georgiev, K. (eds.) Numerical Methods and Applications. NMA 2018. Lecture Notes in Computer Science, vol 11189, pp. 483–490. Springer, Cham. (2019)
Vasilyev, V.B.: On a Digital Version of Pseudo-Differential Operators and Its Applications. In: Dimov, I., Faragó, I., Vulkov, L. (eds.) Finite Difference Methods. Theory and Applications. FDM 2018. Lecture Notes in Computer Science, vol 11386, pp. 596–603. Springer, Cham. (2019)
Vasilyev, V.: The periodic Cauchy kernel, the periodic Bochner kernel, and discrete pseudo-differential operators, AIP Conf. Proc. 1863 140014 (2017)
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Tarasova, O., Vasilyev, V. (2021). Approximation Properties of Discrete Boundary Value Problems for Elliptic Pseudo-Differential Equations. In: Vermolen, F.J., Vuik, C. (eds) Numerical Mathematics and Advanced Applications ENUMATH 2019. Lecture Notes in Computational Science and Engineering, vol 139. Springer, Cham. https://doi.org/10.1007/978-3-030-55874-1_108
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