Case analysis Numerical solution of differential equations with uncertainty and applications

Abstract

Introduction: For the solution of problems that need to be solved exactly. whose solution must be treated by means of numerical methods Objective: The present investigation aims to carry out a study of the numerical methods of Euler and Runge Kutta in order to make an approximation to the solution of random differential equations which use the calculus stochastic referring to the mean square. Methodology: Within the development process, Euler's methodology is analyzed in the first instance within the scalar case and later it is dimensioned to matrix problems, Results: obtaining an analysis of the application of numerical methods to the study of an electrical circuit which is develops with random noise, in the specific case of characteristic and irregular white noises they lead to other types of differential equations with a certain degree of uncertainty called stochastic differential equations. Conclusion: The Euler scheme allows us to conclude that the slow convergence and the restriction aspect of its region of absolute stability allows us to consider other methods where the convergence is greater, thus proposing an additional study of the Runge-Kutta random scheme, being a method superior to that of Euler for which its global order of convergence is fourth.