Application of Homotopy Perturbation Method for Fuzzy Linear Systems and Comparison with Adomian’s Decomposition Method

Algorithm 2

ADM method for FLS.

Given𝛿₀=𝐷_𝐴⁻¹𝑏₁,𝜎₀=𝐷_𝐸⁻¹𝑏₂, and the stopping criterion with tolerance 𝜀>0,

  for 𝑛=1,2,…, until 𝛿_𝑛+1−𝛿_𝑛𝜎≤𝜀,_𝑛+1−𝜎_𝑛≤𝜀,  do

      𝛿_𝑛+1=𝐷_𝐴⁻¹𝐿_𝐴+𝑈_𝐴𝛿_𝑛+𝐷_𝐴⁻¹𝑏₁,

      𝜎_𝑛+1=𝐷_𝐸⁻¹𝐿_𝐸+𝑈_𝐸𝜎_𝑛+𝐷_𝐸⁻¹𝑏₂,

         Obtain 𝑥₋=𝛿_𝑛+1−𝜎_𝑛+12,𝛿𝑥=^𝑛+1+𝜎_𝑛+12.

  End for.