By Guri I. Marchuk

ISBN-10: 9048144442

ISBN-13: 9789048144440

ISBN-10: 9401706212

ISBN-13: 9789401706216

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Extra resources for Adjoint Equations and Analysis of Complex Systems

Example text

However, we can call off the assumption and obtain 1 Jp = jp(cp,x)cpdx, o 1 Jp = j f(x)cp*dx o . 16), Jp will remain as a linear functional of a solution to the adjoint problem 1 Jp = JJ

7) is the sought-for functional. 8) We thus obtain a dual formula for definition of one functional. 8) happens to be more useful in many complex problems, especially if the source function J(x) changes in the variations of the problem while the operator and boundary conditions do not. 7; IJ ~: We can compute this functional using the formula J = OA JJ(x)

11). 13), we obtain two equivalent formulas to compute the functional Jp : Jp =j 1 o p(x)cpdx, Jp =j 1 f(x)cp*dx 0 We have regarded the function p as independent of the solution cp until now. However, we can call off the assumption and obtain 1 Jp = jp(cp,x)cpdx, o 1 Jp = j f(x)cp*dx o . 16), Jp will remain as a linear functional of a solution to the adjoint problem 1 Jp = JJ