# New Approximation Methods Based on Fuzzy Transform for Solving SODEs: II
## Appendix A Two-step algorithm for system of ODEs. ``` INPUT: \(f(t,x,y);g(t,x,y)\); endpoints \(a,b\); integer \(N\); initial condition \(y_{12}\). Step 1 Set \(h=(b-a)/N\); \(X_{1}=x_{12}\); \(Y_{1}=y_{12}\); \(t_{1}=a;k=1,\ldots,N+1\); \(t_{k}=a+(k-1)h\). Step 2 Define the generalized uniform fuzzy partitions as \(\mathbb{B}_{k}(t)=\left(\frac{\sqrt{2}(m+1)}{2(m+1)}\right)\frac{1}{2k}\left(1+ \cos\left(\frac{t-(k-1)}{k}\right)\right)^{m}\). Step 3 Set \(X_{2}=x_{2}\); \(Y_{2}=y_{2}\)



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