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In applied mathematics, methods of mean weighted residuals (MWR) are methods for solving differential equations. The solutions of these differential equations are assumed to be well approximated by a finite sum of test functions . In such cases, any one of a theoretically infinite set of methods of weighted residuals (depending on the choice of ) are applied in an attempt to find which precise value each of the coefficient weight of the corresponding test functions. These coefficients are made to minimize the error between the sum of the test functions and actual solution in a chosen norm. ==Notation of this page== It is often very important to firstly sort out notation used before presenting how this method is executed in order to avoid confusion. * shall be used to denote the solution to the differential equation that the MWR method is being applied to. *Solving the differential equation mentioned shall be set to equate to setting some function called the "residue function" to zero. *Every method of mean weighted residuals involves some "test functions" that shall be denoted by . *The degrees of freedom shall be denoted by . *If the assumed form of the solution to the differential equation is linear (in the degrees of freedom) then the basis functions used in said form shall be denoted by . 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「Method of mean weighted residuals」の詳細全文を読む スポンサード リンク
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