Stability and absolute stability of a three-point difference scheme
Consider a three-point difference scheme -h(-2)Delta((2))y(n) +q(n) (h)y(n) = f(n) (h), n is an element of Z = {0, +/-1, +/-2....}, (1) where h is an element of (0, h(0)), h(0) is a given positive number, Delta((2))y(n) = y(n+1) - 2y(n) + y(n-1), f(h) {f(n) (h)}n is an element of z is an element of L-infinity(h), L-infinity(h) = {f(h) : parallel tof(h)parallel toL(infinity(h)) < infinity}, parallel tof(h)parallel toL(infinity)(h) = sup(nis an element ofZ) \f(n)(h)\. We assume a unique a priori requirement 0 less than or equal to q (h) < infinity for any n is an element of Z and h E (0, h(0)). The main results are a criterion of stability and absolute stability of the difference scheme (1) in the space L-infinity(h). (C) 2003 Elsevier Science Ltd. All rights reserved.
stability absolute stability three-point difference scheme