Design of Finite Difference Method and Neural Network Approach for Casson Nanofluid Flow: A Computational Study

To boost productivity, commercial strategies, and social advancement, neural network techniques are gaining popularity among engineering technical research groups. This work proposes a numerical scheme to solve linear non-linear ordinary differential equations (ODEs). The scheme’s primary benefit included its third-order accuracy in two stages, whereas most examples the literature do not provide stages. was explicit correct third order. stability region consistency analysis of for ODE provided this paper. Moreover, mathematical model heat mass transfer non-Newtonian Casson nanofluid flow is given under effects induced magnetic field, which explored quantitatively using method Levenberg–Marquardt back propagation artificial networks. governing were reduced ODEs suitable similarity transformations later solved by proposed with accuracy. Additionally, approach input output/predicted values given. In addition, inputs velocity, temperature, concentration profiles mapped outputs network. results displayed different types graphs. Absolute error, regression studies, mean square error histogram analyses presented validate suggested networks’ performance. technique currently used on three these four targets. Two hundred points utilized, 140 samples training, 30 validation, testing. These findings demonstrate efficacy networks forecasting optimizing complex systems.