TY - JOUR
TI - A new numerical method for solving two-dimensional variable-order anomalous sub-diffusion equation
AU - Jiang Wei
AU - Guo Beibei
JN - Thermal Science
PY - 2016
VL - 20
IS - 13
SP - 701
EP - 710
PT - Article
AB - The novelty and innovativeness of this paper are the combination of  reproducing kernel theory and spline, this leads to a new simple but  effective numerical method for solving variable-order anomalous sub-diffusion  equation successfully. This combination overcomes the weaknesses of piecewise  polynomials that can not be used to solve differential equations directly  because of lack of the smoothness. Moreover, new bases of reproducing kernel  spaces are constructed. On the other hand, the existence of any ε-approximate  solution is proved and an effective method for obtaining the ε-approximate  solution is established. A numerical example is given to show the accuracy  and effectiveness of theoretical results.