روش عناصر متناهی برای حل مسئلۀ نفوذ غیرخطی معکوس

1. Alifanov O. M., "Inverse Heat Transfer Problems", Springer, New York, (1994). ## 2. Bear J., "Dynamics of Fluids in Porous Media", 2nd edn. Elsevier, New York (1975). ## 3. Beilina L., Johnson C., "A hybrid finite element/difference method for an inverse scattering problem", In Numerical Mathematics and Advanced Applications-ENUMATH, Springer-Verlag (2001). ## 4. Cannon J. R., "The One-Dimensional Heat Equation", Addison-Wesley, Menlo Park, California (1984). ## 5. Cannon J. R., Duchateau, "An inverse Problem for a nonlinear diffusion equation", SIAM J. Appl. Math. 39 (2) (1980) 272-289. ## 6. Cannon J. R., Zachmann D., "Parameter determination in parabolic partial differential equations from overspecified boundary data", Int. J. Eng. Sci. 20 (1982) 779-788. ## 7. Courant R., "Variational methods for the solution of problems of equilibrium and vibrations", Bull, Amer, Math, Soc., 49 (1943) 1-23 . ## 8. Duchateau P., "Monotonicity and uniqueness results in identifying an unknown coefficient in a nonlinear diffusion equation", SIAM J. App. Math. 41 (2) (1981) 310-323. ## 9. El-Azab M. S., Abdelgaber K. M., "Finite element solution of nonlinear diffusion problems", Applied Mathematics and Computation, 217 (2011) 6198-6205. ## 10. Elden L., "A note on the computation of the generalized cross-validation function for ill-conditioned least squares problems", BIT, 24 (1984) 467-472. ## 11. Friedman A., "Partial Differential Equations of Parabolic Type", PrenticeHall, Englewood Cliffs, NJ (1964). ## 12. Golub G. H., Heath M., Wahba G., "Generalized cross-validation as a method for choosing a good ridge parameter", Technometrics. 21 (2) (1979) 215-223 . ## 13. John V., Schmeyer E., "Finite element methods for time dependent convection diffusion reaction equations with small diffusion", Comput. Methods Appl. Mech. Engrg. 198 (2008) 475-494. ## 14. Larsson S., Thomee V., "Partial Differential Equations with Numerical Methods", Springer, (2003). ## 15. Ozisik M. N., "Heat Conduction", Second edition, Wiley, New York (1993). ## 16. Pourgholi R., Rostamian M., "A numerical technique for solving IHCPs using Tikhonov regularization method", Appl. Math. Model. 34 (8) (2010) 2102-2110. ## 17. Foadian S., Pourgholi R., Tabasi S. H., "Cubic B-spline method for the solution of an inverse parabolic system", Applicable Analysis. (2017) 1-28. ## 18. Pourgholi R., Tavallaie N., Foadian S., "Applications of Haar basis method for solving some ill-posed inverse problems", J. Math. Chem. 50(2012) 2317-2337. ## 19. Shidfar A., Nikoofar H. R., "An inverse problem for a linear diffusion equation with nonlinear boundary condition", Appl. Math. Lett. 2 (4) (1989) 385-388. ## 20. Shidfar A., Pourgholi R., "Application of finite difference method to analysis an ill-posed problem", Applied Mathematics and Computation 168 (2) (2005) 1400-1408. ## 21. Shidfar A., Pourgholi R., Ebrahimi M., "A numerical method for solving of a nonlinear inverse diffusion problem", Computers and Mathematics with Applications, 52 (2006) 1021-1030. ## 22. Thomee V., "Galerkin Finite Element Methods for Parabolic Problems", Second edition, Springer, (1997). ## 23. Tikhonov A. N., Arsenin V. Y., "Solution of Ill-Posed Problems", V. H. Winston and Sons, Washington (1977). ## 24. Zlamal M., "Finite element methods for nonlinear parabolic equations", Num. Analysis, 11 (1977) 93-107. ##