Solución Numérica de Ecuaciones Diferenciales Ordinarias no Lineales por el Método de los Incrementos Finitos (MIF). Una Propiedad de las Soluciones

Abstract

In references papers it is presented a singular attribute of the differential equations solution related to FIM, which allows a
very low computational cost version of that methode based upon a two steps problem solving. First step which consists of a small seanl and the second step in which computation is completed by means of recursive procedure, that is, it is not required the simultaneus solution a large seanl.
This paper follows what was presented in reference [1], the FIM application to linear odes. Even with some more complexity it is shown here, that the methode applies also to non linear ode. It is here shown that, even with some more complexity, the methode is appliable to non linear edos with similar observations relative to advantages and disadvantages mentioned in the reference.
The main advantage can be presented as follows:
Taylors computation in MIF can be reduced to the calculation initial values of a recursive sequence.
This have three benefits:
a) Better accuracy conditions of results,
b) Less dense dominium discretization with larger macroelements.
c) Computational lower cost.
Pertinent conceptualizations are operatively presented and an explanatory example is shown.
In references [2,3] conceptual extensions to eddp have been made.