Compact finite difference scheme for the solution of a time fractional partial integro‐differential equation with a weakly singular kernel

[1]  M. Meerschaert,et al.  Finite difference approximations for fractional advection-dispersion flow equations , 2004 .

[2]  Fawang Liu,et al.  A novel implicit finite difference method for the one-dimensional fractional percolation equation , 2011, Numerical Algorithms.

[3]  MEHDI DEHGHAN,et al.  Solution of a partial integro-differential equation arising from viscoelasticity , 2006, Int. J. Comput. Math..

[4]  Chuanju Xu,et al.  Error Analysis of a High Order Method for Time-Fractional Diffusion Equations , 2016, SIAM J. Sci. Comput..

[5]  Tao Tang,et al.  A finite difference scheme for partial integro-differential equations with a weakly singular kernel , 1993 .

[6]  Anatoly A. Alikhanov,et al.  A new difference scheme for the time fractional diffusion equation , 2014, J. Comput. Phys..

[7]  Mingxu Yi,et al.  Legendre wavelets method for the numerical solution of fractional integro-differential equations with weakly singular kernel , 2016 .

[8]  M. Gurtin,et al.  A general theory of heat conduction with finite wave speeds , 1968 .

[9]  Zhi-Zhong Sun,et al.  A compact finite difference scheme for the fractional sub-diffusion equations , 2011, J. Comput. Phys..

[10]  R. K. Miller,et al.  An integrodifferential equation for rigid heat conductors with memory , 1978 .

[11]  Mehdi Dehghan,et al.  An implicit RBF meshless approach for solving the time fractional nonlinear sine-Gordon and Klein–Gordon equations , 2015 .

[12]  Mehdi Dehghan,et al.  A meshless technique based on the local radial basis functions collocation method for solving parabolic–parabolic Patlak–Keller–Segel chemotaxis model , 2015 .

[13]  Da Xu,et al.  A compact difference scheme for a partial integro-differential equation with a weakly singular kernel , 2015 .

[14]  Cui-Cui Ji,et al.  A High-Order Compact Finite Difference Scheme for the Fractional Sub-diffusion Equation , 2014, Journal of Scientific Computing.

[15]  Siu-Long Lei,et al.  High order finite difference method for time-space fractional differential equations with Caputo and Riemann-Liouville derivatives , 2015, Numerical Algorithms.

[16]  Zhibo Wang,et al.  Compact difference schemes for the modified anomalous fractional sub-diffusion equation and the fractional diffusion-wave equation , 2013, J. Comput. Phys..

[17]  Fawang Liu,et al.  Numerical approximations and solution techniques for the space-time Riesz–Caputo fractional advection-diffusion equation , 2011, Numerical Algorithms.

[18]  Li Zhu,et al.  SCW method for solving the fractional integro-differential equations with a weakly singular kernel , 2016, Appl. Math. Comput..

[19]  Han Zhou,et al.  A class of second order difference approximations for solving space fractional diffusion equations , 2012, Math. Comput..

[20]  Da Xu,et al.  Quasi wavelet based numerical method for a class of partial integro-differential equation , 2012, Appl. Math. Comput..

[21]  Mingrong Cui,et al.  Compact finite difference method for the fractional diffusion equation , 2009, J. Comput. Phys..