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Taylor series

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f_{i+1}=f_i+hf'_i+\frac{h^2}{2!}f''_i+\frac{h^3}{3!}f'''_i+...


f_{i-1}=f_i-hf'_i+\frac{h^2}{2!}f''_i-\frac{h^3}{3!}f'''_i+...

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