Numerous applied mathematics and physical applications, such as the simulation of financial mathematics, gas dynamics, nonlinear phenomena in plasma physics, fluid mechanics, ocean engineering, utilize time-fractional generalized Burgers–Fisher equation (TF-GBFE). This describes concept dissipation illustrates how reaction systems can be coordinated with advection. To examine analyze present ev...

The present work deals with the global solvability as well asymptotic analysis of stochastic generalized Burgers–Huxley (SGBH) equation perturbed by a white-in-time and correlated-in-space noise defined in bounded interval $${\mathbb {R}}$$ . We first prove existence unique mild strong solution to SGBH then obtain an invariant measure. Later, we establish two major properties Markovian semigrou...

A fourth order finite-difference scheme in a two-time level recurrence relation is proposed for the numerical solution of the generalized Burgers-Huxley equation. The resulting nonlinear system, which is analyzed for stability, is solved using an improved predictor-corrector method. The efficiency of the proposed method is tested to the kink wave using both appropriate boundary values and condi...

In this work we address the analysis of stationary generalized Burgers-Huxley equation (a nonlinear elliptic problem with anomalous advection) and propose conforming, nonconforming discontinuous Galerkin finite element methods for its numerical approximation. The existence, uniqueness regularity weak solutions are discussed in detail using a Faedo-Galerkin approach fixed-point theory, priori er...