In this work I develop numerical algorithms that can be applied directly to differential equations of the general form f (t, x, x') = 0, without the need to cleared x'. My methods are hybrid algorithms between standard methods of solving differential equations and methods of solving algebraic equations, with which the variable x' is numerically cleared. The application of these methods ranges from the ordinary differential equations of order one, to the more general case of systems of m equations of order n. These algorithms are applied to the solution of different physical-mathematical equations. Finally, the corresponding numerical analysis of existence, uniqueness, stability, consistency and convergence is made, mainly for the simplest case of a single ordinary differential equation of the first order.
Diff selection: Mark the radio boxes of the revisions to compare and hit enter or the button at the bottom.
Legend: (cur) = difference with latest revision, (prev) = difference with preceding revision, m = minor edit.
Published on 27/11/17Submitted on 27/11/17
Volume 1, 2017Licence: CC BY-NC-SA license
Views 37Recommendations 0