This paper discusses the extension of nonlinear diffusion filters to higher derivative orders. While such processes can be useful in practice, their theoretical properties are only partly understood so far. We establish important results concerning L-stability and forwardbackward diffusion properties which are related to well-posedness questions. Stability in the L-norm is proven for nonlinear ...

This paper deals with the problem of determining the multiple roots of nonlinear equations, where the multiplicity of the roots is known. The paper contains some remarks on the optimality of the recently published methods [B. Liu, X. Zhou, A new family of fourth-order methods for multiple roots of nonlinear equations, Nonlinear Anal. Model. Control, 18(2):143–152, 2013] and [X. Zhou, X. Chen, Y...

This paper focuses on the study of oscillatory behavior fourth-order nonlinear neutral delay difference equations. The authors use mathematical techniques, such as Riccati substitution and comparison technique, to explore regularity existence properties solutions these present a new form equation: Δ(a(m)(Δ3z(m))p1−1)+p(m)wp2−1(σ(m))=0, where z(m)=w(m)+q(m)w(m−τ) with following conditions: ∑s=m0...