Numerical methods for equations and its applications This monograph is intended for researchers in computational sciences and as a reference book for an advanced numerical functional analysis or computer science course. The goal is to introduce these powerful concepts and techniques at the earliest possible stage. The reader is assumed to have had basic courses in numerical analysis computer programming computational linear algebra and an introduction to real complex and functional analysis. Although the book is of a theoretical nature with optimization and weakening of existing hypotheses considerations each chapter contains several new theoretical results and important applications in engineering in dynamic economics systems in input output system in the solution of nonlinear and linear differential equations and optimization problem