A numerical method for solving distributed order diffusion equations

Abstract In this letter, a numerical method is proposed for solving distributed order diffusion equations. By using the classical numerical quadrature formulas, the distributed order diffusion equation is approximated by a multi-term time-fractional diffusion equation, which is then solved by the reproducing kernel method. The effectiveness of the numerical scheme is illustrated through two numerical examples.

[1]  S. Li,et al.  A numerical method for singularly perturbed turning point problems with an interior layer , 2014, J. Comput. Appl. Math..

[2]  Fawang Liu,et al.  Compact difference scheme for distributed-order time-fractional diffusion-wave equation on bounded domains , 2015, J. Comput. Phys..

[3]  John T. Katsikadelis,et al.  Numerical solution of distributed order fractional differential equations , 2014, J. Comput. Phys..

[4]  Minggen Cui,et al.  Nonlinear Numerical Analysis in Reproducing Kernel Space , 2009 .

[5]  Boying Wu,et al.  A numerical technique for variable fractional functional boundary value problems , 2015, Appl. Math. Lett..

[6]  Esmail Babolian,et al.  Some error estimates for solving Volterra integral equations by using the reproducing kernel method , 2015, J. Comput. Appl. Math..

[7]  Neville J. Ford,et al.  Distributed order equations as boundary value problems , 2012, Comput. Math. Appl..

[8]  Yury Luchko,et al.  BOUNDARY VALUE PROBLEMS FOR THE GENERALIZED TIME-FRACTIONAL DIFFUSION EQUATION OF DISTRIBUTED ORDER , 2009 .

[9]  Anatoly A. Alikhanov,et al.  Numerical methods of solutions of boundary value problems for the multi-term variable-distributed order diffusion equation , 2013, Appl. Math. Comput..

[10]  M. L. Morgado,et al.  Numerical approximation of distributed order reaction-diffusion equations , 2015, J. Comput. Appl. Math..

[11]  Kai Diethelm,et al.  Numerical analysis for distributed-order differential equations , 2009 .

[12]  N. Aronszajn.  Theory of Reproducing Kernels. , 1950 .

[13]  Fazhan Geng,et al.  Solving a nonlinear system of second order boundary value problems , 2007 .

[14]  X. Y. Li,et al.  Error estimation for the reproducing kernel method to solve linear boundary value problems , 2013, J. Comput. Appl. Math..

[15]  Fazhan Geng,et al.  Solving singular two-point boundary value problem in reproducing kernel space , 2007 .

[16]  Zhi-Zhong Sun,et al.  Some high-order difference schemes for the distributed-order differential equations , 2015, J. Comput. Phys..

[17]  M. Faierman,et al.  Asymptotic formulae for the eigenvalues of a two-parameter ordinary differential equation of the second order , 1972 .