• An implicit finite difference approximation for the solution of the diffusion equation with distributed order in time

      Ford, Neville J.; Morgado, Maria L.; Rebelo, Magda S.; University of Chester, UTAD, Portugal, Universidade Nova de Lisboa, Portugal (Kent State University/Johann Radon Institute for Computational and Applied Mathematics of the Austrian Academy of Sciences, 2015-06-10)
      In this paper we are concerned with the numerical solution of a diffusion equation in which the time order derivative is distributed over the interval [0,1]. An implicit numerical method is presented and its unconditional stability and convergence are proved. A numerical example is provided to illustrate the obtained theoretical results.