Open AccessA CLASS OF S-STEP NON-LINEAR ITERATION SCHEME BASED ON PROJECTION METHOD FOR GAUSS METHOD
Author(s) -
R. Vigneswaran,
S. Kajanthan
Publication year - 2019
Publication title -
advances in mathematical sciences
Language(s) - English
Resource type - Journals
ISSN - 2664-598X
DOI - 10.37516/adv.math.sci.2019.0061
Subject(s) - mathematics , projection (relational algebra) , coefficient matrix , spectral radius , diagonal , matrix (chemical analysis) , iterative method , gauss–seidel method , rate of convergence , gaussian elimination , convergence (economics) , diagonal matrix , projection method , power iteration , nonlinear system , mathematical optimization , algorithm , eigenvalues and eigenvectors , dykstra's projection algorithm , computer science , geometry , channel (broadcasting) , computer network , physics , materials science , quantum mechanics , economics , composite material , gaussian , economic growth
Various iteration schemes are proposed by various authors to solve nonlinear equations arising in the implementation of implicit Runge-Kutta methods. In this paper, a class of s-step non-linear scheme based on projection method is proposed to accelerate the convergence rate of those linear iteration schemes. In this scheme, sequence of numerical solutions is updated after each sub-step is completed. For 2-stage Gauss method, upper bound for the spectral radius of its iteration matrix was obtained in the left half complex plane. This result is extended to 3-stage and 4-stage Gauss methods by transforming the coefficient matrix and the iteration matrix to a block diagonal form. Finally, some numerical experiments are carried out to confirm the obtained theoretical results.
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