A computational method based on Bicubic spline Interpolation for (2+1) dimensional Sobolev and generalize BBMB models

Abstract This paper presents a computational study of the two-dimensional Sobolev and nonlinear generalized Benjamin-Bona-Mahony-Burgers (NGBBMB) equations, which arise in fluid-flow and wave-propagation models. An efficient numerical method based on bicubic spline interpolation is proposed to approximate their solutions. Becouse of two spatial and time variables, first we descritize temporal part using finite difference approche while spatial part is approximated by bicu-bic spline technique. With this strategy, two-dimensional PDEs are transformed into systems of algebraic equations, and a collocation approach is employed to determine the spline coefficients. The numerical results demonstrate that the (1+2) dimensional bicubic spline method is robust and efficient for solving two-dimensional linear and nonlinear PDEs. The L2 and L∞ norms are computed to validate the proposed scheme, confirming its accuracy and effectiveness. The graphical solution profiles demonstrate close agreement between the exact and approximate solutions for all considered problems. MSC Classification: 65D07 , 65M06 , 35G20