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- W68759983 abstract "This chapter discusses the use of the adjoint equation. For every solution, the adjoint equation can be found, and the order of the original equation can be reduced by one. For an n- th order linear differential operator L [·] (shown operating on the function u ( x )) L [ u ( x )] = a 0 xd n u / dx n + a 1 ( x )d n−1 u/dx n−1 + …+ a n -1 ( x ) du / dx + a n ( x ) u then the adjoint of L [·] is defined to be L *[·]. The chapter also highlights that if an operator and its adjoint are identical, then the operator is said to be formally self-adjoint. In this case, the adjoint method does not help to find a solution of the original differential equation. Similar results hold for linear partial differential equations." @default.
- W68759983 created "2016-06-24" @default.
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- W68759983 date "1992-01-01" @default.
- W68759983 modified "2023-09-25" @default.
- W68759983 title "Use of the Adjoint Equation*" @default.
- W68759983 doi "https://doi.org/10.1016/b978-0-12-784391-9.50048-8" @default.
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