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In applied mathematics, methods of mean weighted residuals 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 ϕ i {\displaystyle \phi _{i}}. In such cases, the selected method of weighted residuals is used to find the coefficient value of each corresponding test function. The resulting coefficients are made to minimize the error between the linear combination of test functions, and actual solution, in a chosen norm.
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