An efficient numerical scheme based on Lucas polynomials for the study of multidimensional Burgers-type equations

Abstract We propose a polynomial-based numerical scheme for solving some important nonlinear partial differential equations (PDEs). In the proposed technique, temporal part is discretized by finite difference method together with ? -weighted scheme. Then, approximation of spatial unknown function and its derivatives, we use mixed approach based on Lucas Fibonacci polynomials. With help these approximations, transform equation to system algebraic equations, which can be easily handled. test performance generalized Burgers–Huxley Burgers–Fisher one- two-dimensional coupled Burgers equations. To compare efficiency accuracy scheme, computed $L_{\infty }$ L? , $L_{2}$ xmlns:mml="http://www.w3.org/1998/Math/MathML">L2 root mean square (RMS) error norms. Computations validate that produces better results than other methods. also discussed confirmed stability technique.