Many nonlinear application problems, including weather forecast satellite-orbit tracing, image processing via discrete data, and locating objects through global positioning systems, can be solved numerically by efficient iterative methods with the aid of high-precision modern computers. Mathematical modeling of such real-life nonlinear application problems usually requires efficient and reliable computational algorithms to solve their governing equations arising in a number of areas of applied sciences in addition to engineering, physics, and mathematics. Iterative methods play key roles in solving the nonlinear governing equations in various scientific disciplines that naturally include the subjects relating to linear algebra, geometry, analysis, difference equations, number theory, differential and integral equations, graph theory, statistics, and engineering mathematics as well as nonlinear discrete dynamics and chaos.

The major aim of this special issue is for authors from scientific disciplines to publish their high- quality research as well as review articles that seek recent developments and innovational techniques including grid and cloud computing technologies on iterative methods and their dynamics for nonlinear problems with applications arising in many fields of applied sciences.

Potential topics include but are not limited to the following:

• Root-finding iterative methods for scalar and vector equations
• Recent developments on nonlinear discrete dynamics and chaos
• Nonlinear recurrence relations with applications
• Iterative methods for generalized inverses
• Solving nonlinear (partial) differential equations with iterative methods
• Nonlinear matrix equations
• Fixed point theory with applications to iterative methods
• Initial-boundary value problems for systems of nonlinear equations
• Iterative methods in Banach space settings with convergence analysis
• Stability analysis and basin of attractions of iteration function
• Computational complexity of iterative techniques