Application of Haar Scale-3 wavelet method to the solution of Buckmaster and Chaffee-Infante non-linear PDE

A novel Haar scale-3 wavelet collocation technique is proposed in this study for dealing with a specific type of parabolic Buckmaster second-order non-linear partial differential equation in a dispersive system and Chafee-Infante second-order non-linear partial differential equation (PDE) in a solitary system. Using Haar scale-3 (HSW-3) wavelets, the system approximates the space and time derivatives. To develop both an implicit and explicit analytical model for the dispersive and solitary system, the collocation approach is employed in conjunction with the discretization of space and time variables. We have examined the effectiveness, applicability, and veracity of the proposed computational approach using a variety of numerical problems with nonlinearity and numerous significant source terms. Additionally, the outcomes are graphically presented and organized. We achieved accuracy with the proposed methods even with a small selection of collocation locations.