The purpose of this work is to introduce an efficient, numerical method utilizing Jaiswal–Laguerre functions to tackle the generalized Newell–Whitehead–Segel (NWS) equation.
In this work, the generalized NWS problem is numerically solved using a collocation method and pseudo-operational matrices. The problem is transformed into an algebraic system of equations by approximating the solution using the Jaiswal–Laguerre functions.
To verify theoretical accuracy, the approximation function’s error bounds are thoroughly examined. Several numerical experiments are carried out to confirm the accuracy, robustness and computational efficiency of the proposed method.
The efficacy of the suggested numerical approach is dependent on the choice of Jaiswal–Laguerre parameters, which may need to be adjusted for certain problem conditions, despite the method’s excellent accuracy and resilience. Furthermore, only a small number of numerical experiments have been used to test the approach thus far, and further research is needed to see whether it can be used for more complex or higher-dimensional versions of the NWS equation.
Four distinct cases are given numerical simulations to verify the theoretical results. By comparing the associated maximum absolute errors, the suggested scheme’s superiority over various existing schemes in the literature is demonstrated.
