SILVA, J. D.; http://lattes.cnpq.br/5245691135458819; SILVA, Jarbas Dantas da,
Résumé:
Differential equations consist of a very pro-
addictive to new discoveries. In this field, both Mathematics and Physics interact
especially in history - the study of calculus by Isaac Newton that opens the door to
new related research as well as the dedication to applications by Daniel Bernoulli
were of fundamental importance in the development of the Differential Equations of the
XVIII century. Nowadays many modeling of practical problems in the scientific field—
result in differential equations, among which we highlight the Law of Cooling
Newton and Carbon Dating 14. With respect to the Existence and Uniqueness of
solutions to these equations the importance of the approximation method is highlighted
Picard's successive steps, which consists of approximating the solution of an ODE from
of a sequence of functions. The study of this numerical method becomes interesting
when its importance is perceived in the demonstration of the Existence Theorem itself
and Uniqueness for Ordinary Differential Equations of 1st Order or Picard's Theorem.