Artificial neural network approach for solving strongly degenerate parabolic and burgers-fisher equations

Partial differential equations (PDEs) emerges in modeling innumerable phenomena that applies in science and technology. In this current work, a methodology involving novel iterative technique considering feed-forward neural networks (FNNs) is suggested to extract approximate solution for the second-order nonlinear PDEs with real constant coefficients (RCCs) taking into account initial and boundary conditions. This perspective is designed to grant good approximation on the basis of learning technique which is associated with quasi-Newton rule. The constructed FNN has the regularizing parameters (weights and biases), which can be utilized to make the error function minimal. The construction of the model leads to the satisfaction of the initial and boundary conditions along with the training of FNN which satisfies the PDEs. Numerical experiments with comparisons exhibits the superior behavior of this technique. We have displayed that the proposed algorithm is much more effective than the other numerical method that confers solutions with good universalization and high precision.