A JACOBI WAVE-FORM RELAXATION METHOD FOR ODES

A Jacobi waveform relaxation (WR) method for solving initial value pro blems for ordinary differential equations (ODEs) is presented. In each window the method uses a technique called dynamic fitting and a pair of continuous Runge{Kutta (RK) formulas to produce the initial wavefor m, after which a fixed number of waveform iterates are computed. The r eliability and efficacy of the method are demonstrated numerically by applying it to qualitatively different problems for linear tridiagonal ODEs.