The Multi-scale method for solving nonlinear time space fractional partial differential equations
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Hossein Aminikhah | Mahdieh Tahmasebi | Mahmoud Mohammadi Roozbahani | H. Aminikhah | M. Tahmasebi | M. M. Roozbahani
[1] D. Benson,et al. Application of a fractional advection‐dispersion equation , 2000 .
[2] Stéphane Mallat,et al. A Wavelet Tour of Signal Processing, 2nd Edition , 1999 .
[3] D. Benson,et al. The fractional‐order governing equation of Lévy Motion , 2000 .
[4] Jaideva C. Goswami,et al. Fundamentals of wavelets , 1999 .
[5] O. Vasilyev,et al. A Dynamically Adaptive Multilevel Wavelet Collocation Method for Solving Partial Differential Equations in a Finite Domain , 1996 .
[6] G. Fix,et al. Least squares finite-element solution of a fractional order two-point boundary value problem , 2004 .
[7] Wolfgang Dahmen,et al. Multiscale Wavelet Methods for Partial Differential Equations , 1997 .
[8] I. Podlubny. Fractional differential equations , 1998 .
[9] Enrico Scalas,et al. Waiting-times and returns in high-frequency financial data: an empirical study , 2002, cond-mat/0203596.
[10] Xinxiu Li,et al. Numerical solution of fractional differential equations using cubic B-spline wavelet collocation method , 2012 .
[11] Wolfgang Dahmen,et al. Multiscale Wavelet Methods for Partial Differential Equations, Volume 6 , 1997 .
[12] Wim Sweldens,et al. The Construction and Application of Wavelets in Numerical Analysis , 1995 .
[13] Rina Schumer,et al. Fractional Dispersion, Lévy Motion, and the MADE Tracer Tests , 2001 .
[14] S. Mallat. A wavelet tour of signal processing , 1998 .
[15] Alan D. Freed,et al. Detailed Error Analysis for a Fractional Adams Method , 2004, Numerical Algorithms.
[16] Andrew K. Chan,et al. Fundamentals of Wavelets: Theory, Algorithms, and Applications , 2011 .
[17] Fawang Liu,et al. The fundamental solution and numerical solution of the Riesz fractional advection–dispersion equation , 2008 .
[18] R. Gorenflo,et al. Fractional calculus and continuous-time finance , 2000, cond-mat/0001120.
[19] Rina Schumer,et al. Multiscaling fractional advection‐dispersion equations and their solutions , 2003 .
[20] Donald A. McLaren. Sequential and Localized Implicit Wavelet Based Solvers for Stiff Partial Differential Equations , 2012 .
[21] Fanhai Zeng,et al. Numerical Methods for Fractional Calculus , 2015 .
[22] David A. Benson,et al. Subordinated advection‐dispersion equation for contaminant transport , 2001 .
[23] Peter Richmond,et al. Waiting time distributions in financial markets , 2002 .
[24] Shaher Momani,et al. Non-perturbative analytical solutions of the space- and time-fractional Burgers equations , 2006 .
[25] R. D. Richtmyer,et al. Difference methods for initial-value problems , 1959 .
[26] Xueke Pu,et al. Fractional Partial Differential Equations and their Numerical Solutions , 2015 .
[27] S. Momani,et al. Application of Variational Iteration Method to Nonlinear Differential Equations of Fractional Order , 2006 .
[28] Jan S. Hesthaven,et al. A Wavelet Optimized Adaptive Multi-Domain Method , 1998 .
[29] R. D. Richtmyer,et al. Difference methods for initial-value problems , 1959 .
[30] H. Srivastava,et al. Theory and Applications of Fractional Differential Equations , 2006 .
[31] H. Aminikhah,et al. NUMERICAL SOLUTION FOR THE TIME – SPACE FRACTIONAL PARTIAL DIFFERENTIAL EQUATIONS BY USING THE WAVELET MULTI – SCALE METHOD , 2016 .
[32] J. A. Tenreiro Machado,et al. Discrete-time fractional-order controllers , 2001 .
[33] O. Marichev,et al. Fractional Integrals and Derivatives: Theory and Applications , 1993 .
[34] Siegfried Müller,et al. A multilevel finite volume method with multiscale-based grid adaptation for steady compressible flows , 2009 .
[35] Nicholas K.-R. Kevlahan,et al. An Adaptive Multilevel Wavelet Solver for Elliptic Equations on an Optimal Spherical Geodesic Grid , 2008, SIAM J. Sci. Comput..
[36] Enrico Scalas,et al. Fractional Calculus and Continuous-Time Finance III : the Diffusion Limit , 2001 .
[37] K. Miller,et al. An Introduction to the Fractional Calculus and Fractional Differential Equations , 1993 .
[38] Christian Blatter. Wavelets: A Primer , 1999 .
[39] Xikui Li,et al. Numerical modeling of viscoelastic flows using equal low-order finite elements , 2010 .
[40] M. Meerschaert,et al. Finite difference approximations for fractional advection-dispersion flow equations , 2004 .
[41] S. Momani,et al. Numerical comparison of methods for solving linear differential equations of fractional order , 2007 .
[42] Hari M. Srivastava,et al. The exact solution of certain differential equations of fractional order by using operational calculus , 1995 .