Method of monotonization of nonlinear equations in Banach spaces
Copyright policy )Method of monotonization of nonlinear equations in Banach spaces
Let E be a Banach space with a proper cone, A:E\(\to E\) be a linear bounded operator, and F:E\(\to E\) be a continuous operator. The author suggests a method of two-sided successive approximations for the equation \(u=AF(u)\) of the following form \[ u^{n+1}=(I+\lambda A)^{-1}A(F(u^ n)+\lambda u^ n),\quad u^ 0=\sigma^+,\quad u_{n+1}=(I+\lambda A)^{-1}A(F(u_ n)+\lambda u_ n),\quad u_ 0=\sigma^-, \] where \(\) is a cone segment on which the operator F is \(\lambda\) I-monotonic.
- Institute of Atomic Energy Poland
- Energy Institute United Kingdom
Iterative procedures involving nonlinear operators, Numerical solutions to equations with nonlinear operators, Equations involving nonlinear operators (general), Monotone operators and generalizations, two-sided successive approximations
Iterative procedures involving nonlinear operators, Numerical solutions to equations with nonlinear operators, Equations involving nonlinear operators (general), Monotone operators and generalizations, two-sided successive approximations
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