Modification Fuzzy Intelligent System For Solving Fuzzy Singular Perturbed Mixed Volterra - Fredholm Integro- Partial Differential Equations

Abstract

Through this effort, we have devised a new method using a neuro-fuzzy system. The neuro-fuzzy system method (MNFS) is the name given to this revised technique. We created a numerical technique for using BC to solve partial differential equations (FSPPs). WA suggests an updated approach that uses neural networks to solve singular perturbation problems.

We changed each element in the training set to a second-degree polynomial. For the purpose of solving FSPMV-FIDEs, the modified neuro-fuzzy system (MNFS) is the name given to this altered methodology

The fuzzy neural network's parameters and hidden units' sigmoid function,were determined using the activation function for hyperbolic tangents, which has the formula Q(x) =Q(x) The proposed approach was compared with classical training algorithms and analysis methods. According to our research, the suggested method is notable for its high accuracy, low error rate, and significantly faster speed compared to traditional methods. The recommended approach is illustrated with several instances