A New Numerical Method for Fast Solution of Partial Integro-Differential   Equations
  A new method of numerical solution for partial differential equations is proposed. The method is based on a fast matrix multiplication algorithm. Two-dimensional Poison equation is used for comparison of the proposed method with conventional numerical methods. It was shown that the new method allows for linear growth in the number of elementary addition and multiplication operations with the growth of grid size, as contrasted with quadratic growth necessitated by the standard numerical methods. The proposed method can be easily generalized for any differential equations. 
Pavel Dourbal and Mikhail Pekker
math.NA