Contemporary Iterative Methods with Applications in Applied Sciences

Dear Colleagues,

The unknowns of engineering equations can be functions (difference, differential and integral equations), vectors (systems of linear or non-linear algebraic equations), or real or complex numbers (single algebraic equations with single unknowns). Except for some special cases, the most commonly used solutions methods are iterative; when starting from one or several initial approximations, a sequence is constructed, which converges to a solution of the equation.

To complicate the matter further, many of these equations are non-linear. The local convergence of iterative methods (without and with memory IM for single or multivariate analysis) plays an important role in analyzing their rate of convergence and lowest requirement of presumption. The local convergence is also very important because it reveals the degree of difficulty in selecting initial points for the iterative method. The study of semilocal convergence for an iterative method I Banach spaces is very interesting because just by imposing conditions on the starting point, instead of on the solution, important results can be obtained, such as the existence and uniqueness of the solution, convergence order, a priori error bounds and convergence domains. These results can be applied to the solution of some practical problems arising from Mathematical Biology, Chemistry, Economics, Medicine, Physics, Engineering Science and Scientific Computing which are described by differential equations, partial differential equations and integral equations.

The papers are invited but not limited on the following topics:

1. Iterative methods with and without memory and their applications.
2. Derivative and derivative-free iterative techniques for non-linear systems and their applications.
3. Local and semi-local convergence analysis of non-linear problems and their applications.

Dr. Jai Prakash Jaiswal
Prof. Dr. Juan Ramón Torregrosa Sánchez
Guest Editors

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