In this paper we consider boundary value techniques based on a three-term numerical method for solving initial value problems. The notions of BV-stability and BV-relative stability are introduced in order to clarify the conditions that a three-term scheme must satisfy for solving efficiently initial value problems. In particular we investigate the BV-stability of boundary value methods based on the mid-point rule, on the Simpson method, and on an Adams-type method. The problem of approximating the solution at the final point is approached and an error estimate at this point is given. Among the main features of the boundary value methods studied there is the possibility of employing the same method for an initial value problem with increasing and decreasing modes and the possibility of implementing efficiently boundary value methods on parallel computers.
BOUNDARY-VALUE METHODS AND BV-STABILITY IN THE SOLUTION OF INITIAL-VALUE PROBLEMS
LOPEZ, Luciano;
1993-01-01
Abstract
In this paper we consider boundary value techniques based on a three-term numerical method for solving initial value problems. The notions of BV-stability and BV-relative stability are introduced in order to clarify the conditions that a three-term scheme must satisfy for solving efficiently initial value problems. In particular we investigate the BV-stability of boundary value methods based on the mid-point rule, on the Simpson method, and on an Adams-type method. The problem of approximating the solution at the final point is approached and an error estimate at this point is given. Among the main features of the boundary value methods studied there is the possibility of employing the same method for an initial value problem with increasing and decreasing modes and the possibility of implementing efficiently boundary value methods on parallel computers.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
