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The Schwarz algorithm proceeds as follows:
#Start with approximate solutions ''u''<sup>( 1 )</sup><sub>0</sub> and ''u''<sup>( 2 )</sup><sub>0</sub> of the PDE in subdomains H<sub>1</sub> and H<sub>2</sub> respectively. Initialize ''k'' to
#Calculate ''u''<sup>( ''j'' )</sup><sub>''k'' + 1</sub> = S(''f'',''u''<sup>(3 − ''j'')</sup><sub>''k''</sub>(''x''<sub>''j''</sub>)) with ''j'' = 1,2.
#Increase ''k'' by one and repeat 2 until sufficient precision is achieved.
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