Numerical treatment of nonlinear singular Flierl–Petviashivili systems using neural networks models

In this study, new intelligent computing methodologies have been developed for highly nonlinear singular Flierl–Petviashivili (FP) problem having boundary condition at infinity by exploiting three different neural network models integrated with active-set algorithm (ASA). A modification in the modeling is introduced to cater the singularity, avoid divergence in results for unbounded inputs and capable of dealing with strong nonlinearity. Three models have been constructed in an unsupervised manner for solving the FP equation using log-sigmoid, radial basis and tan-sigmoid transfer functions in the hidden layers of the network. The training of adaptive adjustable variables of each model is carried out with a constrained optimization technique based on ASA. The proposed models have been evaluated on three variants of the two FP equations. The designed models have been examined with respect to precision, stability and complexity through statistics.