This paper is concerned with the backward differential formula or BDF methods for a class of nonlinear 2-delay differential algebraic equations. We obtain two sufficient conditions under which the methods are stable and asymptotically stable. At last, examples show that our methods are true.

Abstract We study a second order Backward Differentiation Formula (BDF) scheme for the numerical approximation of linear parabolic equations and nonlinear Hamilton–Jacobi–Bellman (HJB) equations. The lack monotonicity BDF prevents use well-known convergence results solutions in viscosity sense. first consider one-dimensional uniformly prove stability with respect to perturbations, $$L^2$$ <mml:...

We determine new, more favourable, and in a sense optimal, multipliers for the threeand five-step backward difference formula (BDF) methods. We apply the new multipliers to establish stability of these methods as well as of their implicit–explicit counterparts for parabolic equations by energy techniques, under milder conditions than the ones recently imposed in [4, 1].

We analyze the discretization of the periodic initial value problem for Kuramoto–Sivashinsky type equations with Burgers nonlinearity by implicit– explicit backward difference formula (BDF) methods, establish stability and derive optimal order error estimates. We also study discretization in space by spectral methods.

We consider the periodic initial value problem for the Kuramoto–Sivashinsky (KS) equation. We approximate the solution by discretizing in time by implicit–explicit BDF schemes and in space by a pseudo–spectral method. We present the results of various numerical experiments.

Related DatabasesWeb of Science You must be logged in with an active subscription to view this.Article DataHistorySubmitted: 19 January 2021Accepted: 18 June 2021Published online: 23 September 2021Keywordssix-step BDF method, multipliers, parabolic equations, stability estimate, energy techniqueAMS Subject HeadingsPrimary, 65M12, 65M60; Secondary, 65L06Publication DataISSN (print): 0036-1429ISS...

The present paper describes implementation details of a new implementation of a BDF solver within MATLAB R . It is tuned to be most efficient when applied as a solver within FEMLAB R . The present code aims at a predictable and efficient performance for index-2 differential-algebraic equations arising within the method of lines. The main novelty is the consequent implementation of a predictive ...

This is a survey of essentially normal operators and related developments. There is an overview of Weyl–von Neumann theorems about expressing normal operators as diagonal plus compact operators. Then we consider the Brown–Douglas–Fillmore theorem classifying essentially normal operators. Finally we discuss almost commuting matrices, and how they were used to obtain two other proofs of the BDF t...