An Efficient Approach for Solving Second Order or Higher Ordinary Differential Equations Using ANN

Abstract

In this article, a computational technique called artificial neural networks (ANN’s) merged with sequential quadratic programming (SQP). The feed forward neural networks are used which outperforms in an unsupervised manner. Activation function called Log-sigmoid is applied in the hidden layers of neural networks for the accuracy of results because it is more stable than any other activation function. This approach is best in terms of accuracy in solving linear and non-linear second or forth order ordinary differential equations. The main task is to implement the linear and nonlinear equations with their initial boundary conditions. This article also contains the application of the Jeffery fluid equation which is fourth order differential equation. Different cases of computational complexity in term of time and space are presented. Comparison of exact solution with the referenced techniques shows the correctness of the proposed scheme. Furthermore, the experimental results show the accuracy 99%-99.9% from the other techniques. This system also shows that it is stable at higher values while other systems deviate at higher values from the exact solution and remains unstable. In mathematics models, this technique outperforms to solve the linear and nonlinear differential equations. So, this will help the mathematicians and scientist to solve the higher order differential equations whom their solution does not exist.