Abstract We consider entropy conservative and dissipative discretizations of nonlinear conservation laws with implicit time investigate the influence iterative methods used to solve arising equations. show that Newton’s method can turn an scheme into anti-dissipative one, even when iteration error is smaller than integration error. explore several remedies, which most performant a relaxation te...

this paper deals with scrutinizing the convergence properties of iterative methods to solve linear system of equations. recently, several types of the preconditioners have been applied for ameliorating the rate of convergence of the accelerated overrelaxation (aor) method. in this paper, we study the applicability of a general class of the preconditioned iterative methods under certain conditio...

posed on a finite dimensional Hilbert space V ∼= R equipped with an inner product (·, ·). Here A : V 7→ V is an symmetric and positive definite (SPD) operator, f ∈ V is given, and we are looking for u ∈ V such that (1) holds. The direct method to solve (1) is to form A−1 or the action of A−1. For example, the Gaussian elimination or LU factorization still remains the most commonly used methods ...