Abstract
Throughout this work through the using of a neuro-fuzzy system, we have developed a new technique. This updated approach is known neuro – fuzzy system method (MNFS). to develop a numerical method for resolving (FSPPs) for ordinary differential equations with BC. The activation function for hyperbolic tangents used to determine the hidden units' sigmoid function and the parameters of a fuzzy neural network and its formula is: .Standard training algorithms and analytical techniques were contrasted with the suggested strategy. Our research revealed the provided approach stands out for its excellent accuracy of the results, low error rate, and much faster speed than that of conventional methods. A number of examples are used to demonstrate the suggested strategy.
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