Solution of Stiff Differential Equations & Dynamical Systems Using Neural Network Methods

There are many laws stating the behavior of the physical world involves quantities which are changing with respect to another quantities and the mathematical expressions of such laws are differential equations. There are numbers of problems of various fields like science, engineering-technology, social science etc. involves differential equations. The researchers have developed many analytical and numerical methods for solving various types of differential equations but difficulties are aroused when stiff differential equations as mathematical models are formed. Stiff differential equations are difficult and complex problems to solve analytically and numerically. Many numerical schemes employing digital computers are available for solving stiff ordinary differential equations, partial differential equations and system of stiff differential equations but have revealed many limitations. In this work we have proposed the artificial neural network method for solving such problems of stiff differential equations as the advance trend.