Pitfalls in fast numerical solvers for fractional differential equations
暂无分享,去创建一个
[1] C. Lubich,et al. Fractional linear multistep methods for Abel-Volterra integral equations of the second kind , 1985 .
[2] Kai Diethelm,et al. Multi-order fractional differential equations and their numerical solution , 2004, Appl. Math. Comput..
[3] Anne Greenbaum,et al. Iterative methods for solving linear systems , 1997, Frontiers in applied mathematics.
[4] J. Lambert. Computational Methods in Ordinary Differential Equations , 1973 .
[5] Ernst Hairer,et al. Fast numerical solution of weakly singular Volterra integral equations , 1988 .
[6] Alan D. Freed,et al. Fractional-order Viscoelasticity (FOV): Constitutive Development Using the Fractional Calculus: First Annual Report , 2002 .
[7] I. Podlubny. Fractional differential equations , 1998 .
[8] R. Bagley,et al. On the Appearance of the Fractional Derivative in the Behavior of Real Materials , 1984 .
[9] Å. Björck,et al. Solution of Vandermonde Systems of Equations , 1970 .
[10] N. Ford,et al. A Predictor-Corrector Approach for the Numerical Solution of Fractional Differential Equations , 2013 .
[11] Alan D. Freed,et al. On the Solution of Nonlinear Fractional-Order Differential Equations Used in the Modeling of Viscoplasticity , 1999 .
[12] N. Levinson,et al. A nonlinear Volterra equation arising in the theory of superfluidity , 1960 .
[13] Å. Björck. Solving linear least squares problems by Gram-Schmidt orthogonalization , 1967 .
[14] Y. Saad,et al. GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems , 1986 .
[15] G. Joulin. Point-Source Initiation of Lean Spherical Flames of Light Reactants: An Asymptotic Theory , 1985 .
[16] H. Walker. Implementation of the GMRES method using householder transformations , 1988 .
[17] O. Marichev,et al. Fractional Integrals and Derivatives: Theory and Applications , 1993 .
[18] Kai Diethelm,et al. Numerical solution of fractional order differential equations by extrapolation , 1997, Numerical Algorithms.
[19] K. Diethelm. AN ALGORITHM FOR THE NUMERICAL SOLUTION OF DIFFERENTIAL EQUATIONS OF FRACTIONAL ORDER , 1997 .
[20] M. Caputo. Linear Models of Dissipation whose Q is almost Frequency Independent-II , 1967 .
[21] Nicholas J. Higham,et al. Error analysis of the Björck-Pereyra algorithms for solving Vandermonde systems , 1987 .
[22] The exponential Vandermonde matrix , 2000 .
[23] Neville J. Ford,et al. The numerical solution of fractional differential equations: Speed versus accuracy , 2001, Numerical Algorithms.
[24] Christopher T. H. Baker,et al. Stability barriers to the construction of { ρ,σ }-reducible and fractional quadrature rules , 1988 .
[25] Louis B. Rall,et al. Automatic Differentiation: Techniques and Applications , 1981, Lecture Notes in Computer Science.
[26] E. Hairer,et al. Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems , 1993 .
[27] N. Ford,et al. Analysis of Fractional Differential Equations , 2002 .
[28] Yousef Saad,et al. Iterative methods for sparse linear systems , 2003 .
[29] Ernst Hairer,et al. Solving Ordinary Differential Equations I: Nonstiff Problems , 2009 .
[30] N. Ford,et al. Numerical Solution of the Bagley-Torvik Equation , 2002, BIT Numerical Mathematics.
[31] Alan D. Freed,et al. Detailed Error Analysis for a Fractional Adams Method , 2004, Numerical Algorithms.
[32] Francesco Mainardi,et al. Fractional Calculus: Some Basic Problems in Continuum and Statistical Mechanics , 2012, 1201.0863.
[33] C. Lubich. Discretized fractional calculus , 1986 .
[34] F. Mainardi,et al. Fractals and fractional calculus in continuum mechanics , 1997 .