A NUMERICAL ALGORITHM FOR SOLVING A PARABOLIC PROBLEM BASED ON QUASI-MONTH CARLO METHOD

A kind of quasi-Monte Carlo method called Haselgroves method has been used for the evaluation of the multiple integral over hypercuble [0.1]p. This method is implemented to solve an initial value problem of the heat equation. Sugihara and Murota proposed the use of the weight function The error bound of their method is of the order O(1/Nk) where N is the number of p-dimensional quasi-random vectors while it is O(N-r), r ≥1 for Haselgoroves method. A numerical algoritm is Used to generate quasi-random vectors. The error table demonstrates the efficiency of the presented algorithm.

Keywords:

quasi Monte Carlo method , initial value problem of the heat equation Haselgroves method , irrational numbers , multiple integral