The Higher Accuracy Fourth-Order IADE Algorithm

Algorithm 1

The IADEMF4 sequential algorithm.

begin

  determine the parameters 𝑚,𝑟,Δ𝑡,Δ𝑥,𝜆,𝜀,𝑇

  determine initial conditions 𝑢_𝑖^(𝑝)

  determine exact solutions 𝑈_𝑖 at time level 𝑇

  while (time level <𝑇)

     determine boundary conditions

     for 𝑖=2 to 𝑖=𝑚−1

        compute 𝑓_𝑖 (refer to (9))

     end-for

        set iteration = 0

        while (convergence conditions are not satisfied)

         for 𝑖=2 to 𝑖=𝑚−1

        compute 𝑢_𝑖^(𝑝+1/2) (refer to (22))

         end-for

         for 𝑖=2 to 𝑖=𝑚−1

        compute 𝑢_𝑖^(𝑝+1) (refer to (23))

         end-for

         test for convergence:

         compute 𝑒_𝑖←𝑢_𝑖^(𝑝+1)−𝑢_𝑖^(𝑝)

         if (max𝑒_𝑖<𝜀)

         then 𝑢_𝑖^(𝑝)←𝑢_𝑖^(𝑝+1)

         add 1 to iteration (if necessary)

        end-while

  end-while

  for 𝑖=2 to 𝑖=𝑚−1

     determine average absolute error, root mean

     square error and maximum error

  end-for

end