УДК 519.6

І. БОРАЧОК
Львівський національний університет імені Івана Франка, Львів, Україна,
 ihor.borachok@lnu.edu.ua

О. ПАЛЯНИЦЯ
Львівський національний університет імені Івана Франка, Львів, Україна,
 oksana.palianytsia@lnu.edu.ua

Р. ХАПКО
Львівський національний університет імені Івана Франка, Львів, Україна,
 roman.chapko@lnu.edu.ua

МЕТОД РАДІАЛЬНИХ БАЗИСНИХ ФУНКЦІЙ
ДЛЯ РОЗВ’ЯЗУВАННЯ ІНТЕГРО-ДИФЕРЕНЦІАЛЬНОГО
РІВНЯННЯ ДИФУЗІЇ З НЕЛОКАЛЬНИМИ ЕФЕКТАМИ

СПИСОК ЛІТЕРАТУРИ

1. Ewing R.E., Lazarov R.D., Lin Y. Finite volume element approximations of nonlocal in time one-dimensional flows in porous media. Computing. 2000. Vol. 64, Iss. 2. P. 157–182. doi.org/10.1007/s006070050007.


2. Kot M., Medlock J. Spreading disease: integro-differential equations old and new. Mathematical Biosciences. 2003. Vol. 184, Iss. 2. P. 201–222. doi.org/10.1016/S0025-5564(03)00041-5.


3. Amadori A.L. Nonlinear integro-differential evolution problems arising in option pricing: A viscosity solutions approach. Differential Integral Equations. 2003. Vol. 7. P. 787–811. dx.doi.org/10.57262/die/1356060597.


4. Briani M., La Chioma C., Natalini R. Convergence of numerical schemes for viscosity solutions to integro-differential degenerate parabolic problems arising in financial theory. Numer. Math. 2004. Vol. 98, Iss. 4. P. 607–646. doi.org/10.1007/s00211-004-0530-0.


5. Chapko R., Palianytsia O. On the boundary-domain integrals approach for a partial integro-differential equation. Visn. Lviv. un-tu. Ser. prykl. matem. ta inf. 2022. Vol. 22. P. 38–44. dx.doi.org/10.30970/vam.2022.30.11432.


6. Brunner H., Yan N. Finite element methods for optimal control problems governed by integral equations and integro-differential equations. Numer. Math. 2005. Vol. 101, Iss. 1. P. 1–27. doi.org/10.1007/s00211-005-0608-3.


7. Shakeri F., Dehghan M. A high order finite volume element method for solving elliptic partial integro-differential equations. Applied Numerical Mathematics. 2013. Vol. 65. P. 105–118. doi.org/10.1016/j.apnum.2012.10.002.


8. Borachok I., Chapko R., Johansson B.T. Numerical solution of a Cauchy problem for Laplace equation in 3-dimensional domains by integral equations. Inverse Probl. Sci. Eng. 2016. Vol. 24, Iss. 9. P. 1550–1568. doi.org/10.1080/17415977.2015.1130042.


9. Gathungu D.K., Borzi A. Multigrid solution of an elliptic Fredholm partial integro-differential equation with a Hilbert–Schmidt integral operator. Applied Mathematics. 2017. Vol. 8, N 7. P. 967–986. doi.org/10.4236/am.2017.87076.


10. Gathungu D., Bebendorf M., Borzi A. Hierarchical-matrix method for a class of diffusiondominated partial integro-differential equations. Numer Linear Algebra Appl. 2022. Vol. 29, Iss. 2. doi.org/10.1002/nla.2410.


11. Kansa E.J. Multiquadrics — A scattered data approximation scheme with applications to computational fluid-dynamics — II. Solutions to parabolic, hyperbolic and elliptic partial differential equations. Computers & Mathematics with Applications. 1990. Vol. 19, Iss. 8–9. P. 147–161. doi.org/10.1016/0898-1221(90)90271-K .


12. Kress R. Numerical integration. In: Numerical analysis. Graduate texts in mathematics. Vol. 181. New York: Springer, 1998. doi.org/10.1007/978-1-4612-0599-9_9.


13. Chen C.S., Dou F., Karageorghis A. A novel RBF collocation method using fictitious centres. Applied Mathematics Letters. 2020. Vol. 101. Article number 106069. doi.org/10.1016/j.aml.2019.106069.


14. Fasshauer G.E., Zhang J.G. On choosing “optimal” shape parameters for RBF approximation. Numerical Algorithms. 2007. Vol. 45, Iss. 1–4. P. 345–368. doi.org/10.1007/ s11075-007-9072-8.


15. Holland J.H. Adaptation in natural and artificial systems: An introductory analysis with applications to biology, control, and artificial intelligence. MIT Press, 1992. doi.org/10.7551/mitpress/1090.001.0001.


16. Michalewicz Z. Genetic algorithms + data structures = evolution programs. 3rd ed. Berlin: Springer-Verlag, 1996. 387 p. doi.org/10.1007/978-3-662-03315-9.


17. Larsson E., Fornberg B. A numerical study of some radial basis function based solution for elliptic PDEs. Comput. Math. Appl. 2003. Vol. 46, Iss. 5–6. P. 891–902. doi.org/10.1016/ S0898-1221(03)90151-9.


18. Ma Z., Li X., Chen C.S. Ghost point method using RBFs and polynomial basis functions. Applied Mathematics Letters. 2021. Vol. 111. Article number 106618. doi.org/10.1016/j.aml.2020.106618.


19. Koushki M., Jabbari E., Ahmadinia M. Evaluating RBF methods for solving PDEs using Padua points distribution. Alexandria Engineering Journal. 2020. Vol. 59, Iss. 5. P. 2999–3018. doi.org/10.1016/j.aej.2020.04.047.


20. Jankowska M.A., Karageorghis A., Chen C.S. Improved Kansa RBF for the solution of nonlinear boundary value problems. Eng. Anal. Bound. Elem. 2018. Vol. 87. P. 173–183. doi.org/10.1016/j.enganabound.2017.11.012.