A numerical approach to approximation for an ultraparabolic equation

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Khoa, Vo Anh; Lan, Le Trong; Ngoc, Nguyen Thi Yen; Tuan, Nguyen Huy;
(2014)
  • Subject: 65L12, 65L80, 34A45, 34G20 | Mathematics - Spectral Theory | Mathematics - Analysis of PDEs | Mathematics - Numerical Analysis

We study the following ultraparabolic equation \[ \frac{\partial}{\partial t}u\left(t,s\right)+\frac{\partial}{\partial s}u\left(t,s\right)+\mathcal{L}u\left(t,s\right)=f\left(u\left(t,s\right),t,s\right),\quad\left(t,s\right)\in\left(0,T\right)\times\left(0,T\right), \... View more
  • References (23)
    23 references, page 1 of 3

    1. F. Ternat, O. Orellana, P. Daripa, Two stable methods with numerical experiments for solving the backward heat equation, Applied Numerical Mathematics 61 (2011) 266-284.

    2. N. H. Tuan, Stability estimates for a class of semi-linear ill-posed problems, Nonlinear Analysis: Real World Applications 14 (2013) 1203-1215.

    3. G. Akrivis, M. Crouzeix, and V. Thomee, Numerical methods for ultraparabolic equations, Calcolo, vol. 31, no. 3-4, pp. 179{190, 1994.

    4. Fadugba S. E., Edogbanya O. H., Zelibe S. C., Crank Nicolson Method for Solving Parabolic Partial Di erential Equations, International Journal of Applied Mathematics and Modeling, Vol.1, No. 3, 8-23, 2013.

    5. F. Zouyed, F. Rebbani, A modi ed quasi-boundary value method for an ultraparabolic ill-posed problem, J. Inverse Ill-Posed Probl., Volume 0, 1569-3945, 2014.

    6. A. Ashyralyev and S. Yilmaz, An Approximation of Ultra-Parabolic Equations, Abstract and Applied Analysis, vol. 2012, Article ID 840621, 14 pages, 2012.

    7. D. D. Trong, N. T. Long, A. P. N. Dinh, Nonhomogeneous heat equation: Identi cation and regularization for the inhomogeneous term, J. Math. Anal. Appl. 312 (2005) 93{104.

    8. Q. Deng , T. G. Hallam , An age structured population model in a spatially heterogeneous environment: Existence and uniqueness theory, Nonlinear Anal. 2006; 65, 379-394.

    9. M. D. Francesco, A. Pascucci, A continuous dependence result for ultraparabolic equations in option pricing, J. Math. Anal. Appl. 336 (2007) 1026{1041.

    10. A. I. Kozhanov, On the Solvability of Boundary Value Problems for Quasilinear Ultraparabolic Equations in Some Mathematical Models of the Dynamics of Biological Systems, Journal of Applied and Industrial Mathematics, 2010, Vol. 4, No. 4, pp. 512{525.

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