Using a cubic B-spline method in conjunction with a one-step optimized hybrid block approach to solve nonlinear partial differential equations

Abstract In this paper, we develop an optimized hybrid block method which is combined with a modified cubic B-spline method, for solving non-linear partial differential equations. particular, it will be applied three well-known problems, namely, the Burgers equation, Buckmaster equation and FitzHugh–Nagumo equation. Most of developed methods in literature equations have not focused on optimizing time step-size very small value must considered to get accurate approximations. The motivation behind development work overcome trade-off up much extent using larger without compromising accuracy. proved A-stable convergent. Furthermore, obtained numerical approximations been compared exact solutions available found adequate. quasilinearization or filtering techniques, results viscosity coefficient are accurate. We that combination two computationally efficient PDEs.