There are many areas of practical mathematics that use partial differential equations (PDEs), such as quantum physics, hydrodynamics, elasticity, and electromagnetic theory. The analytical behavior of these equations is a rather involved process and requires the application of advanced mathematical methods. The wavelet is a powerful mathematical tool that plays an important role in science and technology.
The Burgers-Fisher equation is a non-linear partial differential equation and has important applications in financial mathematics, gas dynamics, traffic flow, number theory, heat conduction, and elasticity, among many other problems in applied mathematics and physics. In this paper, we presented a wavelet-based lifting scheme for the numerical solution of Burgers-Fisher equations using orthogonal and biorthogonal wavelet filter coefficients. The numerical results obtained by this scheme are compared with the exact solution to demonstrate the accuracy and also speed up convergence in less computational time as compared with the existing scheme. Some test problems are presented about the applicability and validity of the scheme.