TY - JOUR
T1 - VARIATIONAL METHODS FOR APPROXIMATING SOLUTIONS OF DEL 2 u(x) equals f(x) plus k(x)u(x) AND GENERALIZATIONS.
AU - McClendon, Marvin
AU - Rabitz, Herschel
PY - 1986
Y1 - 1986
N2 - The iterative procedure of Guy, Sales, Brami-Depaux, and Joly-Cabaret (GSBJ) for approximately solving equations of the form DEL **2u equals f plus ku is analyzed and generalized from the viewpoint of the calculus of variations. The variational approach is tested on three simple example problems and the numerical results are seen to compare favorably with those of GSBJ and with the exact solution. In addition, two new variational functionals are derived, various iteration schemes are discussed, the method is extended to more general equations, and further connections with other work are established.
AB - The iterative procedure of Guy, Sales, Brami-Depaux, and Joly-Cabaret (GSBJ) for approximately solving equations of the form DEL **2u equals f plus ku is analyzed and generalized from the viewpoint of the calculus of variations. The variational approach is tested on three simple example problems and the numerical results are seen to compare favorably with those of GSBJ and with the exact solution. In addition, two new variational functionals are derived, various iteration schemes are discussed, the method is extended to more general equations, and further connections with other work are established.
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U2 - 10.1137/0146035
DO - 10.1137/0146035
M3 - Article
AN - SCOPUS:0022768111
SN - 0036-1399
VL - 46
SP - 525
EP - 544
JO - SIAM Journal on Applied Mathematics
JF - SIAM Journal on Applied Mathematics
IS - 4
ER -