ITERATIVE SCHEMES FOR SOLVING NEW SYSTEM OF GENERAL EQUATIONS

In this paper, we consider a new system of general equations, which can be used to study the odd-order and nonsymmetric boundary value problems. It is shown that LaxMilgram Lemma and Reisz-Fréchet representation theorem can be obtained as special cases. We use the auxiliary principle technique to prove the existence of a solution to the general equations. This technique is also used to suggest some new iterative methods. The convergence analysis of the proposed methods is analyzed under some mild conditions. Ideas and techniques of this paper may stimulate further research. © 2022, Politechnica University of Bucharest. All rights reserved.