H. Azari and F. Parzlivand, Determination of the coefficient in the advection diffusion equation using collocation and radial basis function, Univ. J. Integral Equations 2 (2014) 20--29.
E. C. Baran, Numerical procedures for determining of an unknown parameter in parabolic equation, Appl. Math. Comput. 162 (2005), no. 3, 1219--1226.
D. Brown, L. Ling, E. Kansa and J. Levesley, On approximate cardinal preconditioning methods for solving PDEs with radial basis functions, Eng. Anal. Bound. Elem. 29 (2005) 343--353.
M. D. Buhmann and C. A. Micchelli, Multiquadric interpolation improved. Advances in the theory and applications of radial basis functions, Comput. Math. Appl. 24 (1992), no. 12, 21--25.
J. R. Cannon and Y. Lin, Determination of parameter $p(t)$ in H\"older classes for some semilinear parabolic equations, Inverse Problems 4 (1988), no. 3, 595--606.
J. R. Cannon and Y. Lin, An inverse problem of finding a parameter in a semi-linear heat equation, J. Math. Anal. Appl. 145 (1990), no. 2, 470--484.
J. R. Cannon, Y. Lin and S. Xu, Numerical procedures for the determination of an unknown coefficient in semi-linear parabolic differential equations, Inverse Problems 10 (1994), no. 2, 227--243.
J. R. Cannon, Y. Lin and S. Wang, Determination of source parameter in parabolic equations, Meccanica 27 (1992) 85--94.
J. R. Cannon and H. M. Yin, Numerical solutions of some parabolic inverse problems, Numer. Methods Partial Differential Equations 2 (1990), no. 2, 177--191.
R. E. Carlson and T. A. Foley, Interpolation of track data with radial basis methods, Comput. Math. Appl. 24 (1992), no. 12, 27--34.
S. Chantrasirivan, Cartesian grid method using radial basis functions for solving Poisson, Helmholtz, and diffusion convection equations, Eng. Anal. Bound. Elem. 28 (2004) 1417--1425.
W. Chen and M. Tanaka, A meshless, integration-free and boundary only RBF technique, Comput. Math. Appl. 4 (2002), no. 3-5, 379--391.
C. K. Chiu, J. Stoeckler and J. D. Ward, Analytic wavelets generated by radial functions, Adv. Comput. Math. 5 (1996), no. 1, 95--123.
F. Davoodi, A. Abbas Nejad, A. Shahrezaee and M. J. Maghrebi, Control parameter estimation in a semi-linear parabolic inverse problem using a high accurate method, Appl. Math. Comput. 218 (2011), no. 5, 1798--1804.
M. Dehghan, Numerical solution of one-dimensional parabolic inverse problem, Appl. Math. Comput. 136 (2003), no. 2-3, 333--344.
M. Dehghan, Determination of a control parameter in the two-dimensional diffusion equation, Appl. Numer. Math. 37 (2001), no. 4, 489--502.
M. Dehghan, An inverse problem of finding a source parameter in a semilinear parabolic equation, Appl. Math. Model. 25 (2001) 743--754.
M. Dehghan, Determination of a control function in three-dimensional parabolic equations, Math. Comput. Simulation 61 (2003), no. 2, 89--100.
M. Dehghan, Finding a control parameter in one-dimensional parabolic equation, Appl. Math. Comput. 135 (2003), no. 2-3, 491--503.
M. Dehghan and A. Shokri, A meshless method for numerical solution of the one-dimensional wave equation with an integral condition using radial basis functions, Numer. Algorithms 52 (2009), no. 3, 461--477.
A. Fatullayev and E. Can, Numerical procedures for determining unknown source parameter in parabolic equations, Math. Comput. Simulation 54 (2000), no. 1-3, 159--167.
R. Franke, A Critical Comparison of Some Methods for Interpolation of Scattered Data, PhD thesis, Naval Postgraduate School Monterey, California, 1979.
R. L. Hardy, Multiquadratic equation of topography and other irregular surfaces, J. Geophys. Res. 76 (1971) 1905--1915.
R. L. Hardy, Theory and applications of the multiquadric biharmonic method: 20 years of discovery, Comput. Math. Appl. 19 (1990), no. 8-9, 163--208.
S. U. Islam, S. Haqb and A. Ali, A meshfree method for the numerical solution of the RLW equation, J. Comput. Appl. Math. 223 (2009), no. 2, 997--1012.
E. Kansa and Y. C. Hon, Circumventing the ill-conditioning problem with multiquadric radial basis functions: applications to elliptic partial differential equations, Comput. Math. Appl. 39 (2000), no. 7-8, 123--137.
A. J. Khattak, S. I. A. Tirmizi and S. U. Islam, Application of meshfree collocation method to a class of nonlinear partial differential equations, Eng. Anal. Bound. Elem. 33 (2009), no. 5, 661--667.
E. Kreyszig, Introductory Functional Analysis with Applications, John Wiley \& Sons Press, New York, 1978.
J. Li, Application of radial basis meshless methods to direct and inverse biharmonic boundary value problems, Commun. Numer. Methods Eng. 21 (2005), no. 4, 169--182.
S. Liu and R. Triggiani, Global uniqueness and stability in determining the damping and potential coefficients of an inverse hyperbolic problem, Nonlinear Anal. Real World Appl. 12 (2011), no. 3, 1562--1590.
N. Mai-Duy and T. Tran-Cong, Numerical solution of differential equations using multiquadric radial basis function networks, Neural Netw. 14 (2001) 185--199.
J. A. MacBain and J. B. Bednar, Existence and uniqueness properties for the one-dimensional magnetotellurics inversion problem, J. Math. Phys. 27 (1986), no. 2, 645--649.
K. Parand, S. Abbasbandy, S. Kazem and J. A. Rad, A novel application of radial basis functions for solving a model of first-order integro-ordinary differential equation, Commun. Nonlinear Sci. Numer. Simul. 16 (2011), no. 11, 4250--4258.
F. Parzlivand and A. M. Shahrezaee, Numerical solution of an inverse reaction diffusion problem via collocation method based on radial basis functions, Appl. Math. Model. 39 (2015), no. 13, 3733--3744.
F. Parzlivand, A. M. Shahrezaee, Gaussian radial basis functions for the solution of an inverse problem of mixed parabolic-hyperbolic type, Eur. J. Pure Appl. Math. 8 (2015), no. 2, 239--254.
A. I. Prilepko and V. V. Soloev, Solvability of the inverse boundary value problem of finding a coefficient of a lower order term in a parabolic equation, J. Differential Equ. 23 (1987) 136--143.
H. Power, M. Zerroukat and C. Chen, A numerical method for heat transfer problems using collocation and radial basis functions, Internat. J. Numer. Methods Engrg. 42 (1998) 1263--1278.
A. G. Ramm, An inverse problem for the heat equation, Proc. Roy. Soc. Edinburgh Sect. 123 (1993), no. 6, 973--976.
A. G. Ramm, Mathematical and Analytical Techniques with Application to Engineering, Springer, NewYork, 2005.
S. Rippa, An algorithm for selecting a good value for the parameter $c$ in radial basis function interpolation, Adv. Comput. Math. 11 (1999), no. 2-3, 193--210.
S. A. Sarra, Adaptive radial basis function method for time dependent partial differential equations, Appl. Numer. Math. 54 (2005), no. 1, 79--94.
C. Shu, H. Ding, and K. S. Yeo, Solution of partial differential equations by a global radial basis function-based differential quadrature method, Eng. Anal. Bound. Elem. 28 (2004) 1217--1226.
W. Wang, B. Han and M. Yamamoto, Inverse heat problem of determining time-dependent source parameter in reproducing kernel space, Nonlinear Anal. Real World Appl. 14 (2013), no. 1, 875--887.
S. Wang and Y. Lin, A finite-difference solution to an inverse problem for determining a control function in a parabolic partial differential equation, Inverse Problems 5 (1989), no. 4, 631--640.
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