To numerical methods for solving multidimensional integro-differential equations
Автор: Beshtokova Z.V.
Журнал: Вестник Бурятского государственного университета. Математика, информатика @vestnik-bsu-maths
Рубрика: Вычислительная математика
Статья в выпуске: 3, 2023 года.
Бесплатный доступ
The third boundary value problem for a multidimensional convection-diffusion equation with memory effect and non-local (integral) source is investigated. To solve numerically the multidimensional problem, a locally one-dimensional difference scheme is constructed, the essence of the idea of which is to reduce the transition from layer to layer to sequential solving of a number of onedimensional problems in each of the coordinate directions. Using the method of energy inequalities for the solution of a locally one-dimensional difference scheme, an a priori estimate is obtained. The main research method is the method of energy inequalities. An a priori estimate of the LOS solution is obtained, from which follow uniqueness, stability, and convergence of the solution of the difference problem to the solution of the original differential problem at a rate equal to the approximation error. Numerical experiments were carried out.
Third initial-boundary value problem, locally one-dimensional scheme (los), a priori estimate, difference scheme, parabolic equation, integro-differential equation, equation with memory, equation with non-local (integral) source
Короткий адрес: https://sciup.org/148327261
IDR: 148327261 | DOI: 10.18101/2304-5728-2023-3-34-52
Список литературы To numerical methods for solving multidimensional integro-differential equations
- Grasselli M. Uniform attractors of nonautonomous dynamical systems with memory // Progress in nonlinear differential equations and their applications. Basel: Birkhauser Verlag. 2002. Vol. 50. P. 155–178. URL: https://link.springer.com/chapter/10.1007/978-3-0348-8221-7_9.
- Coleman B. D, Gurtin M. E. Equipresence and costitutive equations for rigid heat conductors // Math. Phys. 1967. Vol. 18. P. 199–208. URL: https://link.springer.com/article/10.1007/bf01596912.
- Gurtin M. E, Pipkin A. C. A general theory of heat conduction with finite wave speeds // Arch. Rational Mech. Anal. 1968. Vol. 31. P. 113–126. URL: https://link.springer.com/article/10.1007/bf00281373.
- Fabrizio M., Morro A. Mathematical problems in linear viscoelasticity. Philadelphia: SIAM Studies Appl. Math. 1992.
- Renardy M., Hrusa W. J., Nohel J. A. Mathematical problems in viscoelasticity. New York: Longman Scientific and Technical, 1987. 273 p.
- Berry E. X. Cloud Droplet Growth by Collection // J. Atmos. Sci. 1967. Vol. 24. P. 688–701.
- Berry E. X., Reinharolt R. L. An Analysis of Cloud Drop Growth by Collection: Part 2. Single initial Distributions // J. Atmos. Sci. 1974. Vol. 31. P. 1825–1837.
- Douglas J., Rachford H. H. On the numerical solution of heat conduction problems in two and three space variables // Trans. Amer. Math. Soc. 1956. Vol. 82, 2. P. 421–439. URL: https://www.ams.org/journals/tran/1956-082-02/S0002-9947-1956-0084194-4/.
- Peaceman D. W., Rachford H. H. The numerical solution of parabolic and elliptic differential equations // J. Industr. Math. Soc. 1955. Vol. 3, 1. P. 28–41. URL: https://epubs.siam.org/doi/10.1137/0103003.
