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In mathematics, the additive Schwarz method, named after Hermann Schwarz, solves a boundary value problem for a partial differential equation approximately by splitting it into boundary value problems on smaller domains and adding the results. == Overview == Partial differential equations (PDEs) are used in all sciences to model phenomena. For the purpose of exposition, we give an example physical problem and the accompanying boundary value problem (BVP). Even if the reader is unfamiliar with the notation, the purpose is merely to show what a BVP looks like when written down. :(Model problem) The heat distribution in a square metal plate such that the left edge is kept at 1 degree, and the other edges are kept at 0 degree, after letting it sit for a long period of time satisfies the following boundary value problem: ::''f''''xx''(''x'',''y'') + ''f''''yy''(''x'',''y'') = 0 ::''f''(0,''y'') = 1; ''f''(''x'',0) = ''f''(''x'',1) = ''f''(1,''y'') = 0 :where ''f'' is the unknown function, ''f''''xx'' and ''f''''yy'' denote the second partial derivatives with respect to ''x'' and ''y'', respectively. Here, the domain is the square () × (). This particular problem can be solved exactly on paper, so there is no need for a computer. However, this is an exceptional case, and most BVPs cannot be solved exactly. The only possibility is to use a computer to find an approximate solution. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Additive Schwarz method」の詳細全文を読む スポンサード リンク
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