Analytical and Numerical Results for the Diffusion-Reaction Equation When the Reaction Coefficient Depends on Simultaneously the Space and Time Coordinates

We utilize the travelling-wave Ansatz to obtain novel analytical solutions linear diffusion–reaction equation. The reaction term is a function of time and space simultaneously, firstly in Lorentzian form secondly cosine form. new contain Heun functions first case Mathieu for second case, therefore are highly nontrivial. use these test some non-conventional explicit stable numerical methods against standard implicit methods, where latter algebraic equation system solved by preconditioned conjugate gradient GMRES solvers. After this verification, we also calculate transient temperature 2D surface subjected cooling effect wind, which again. that can reach accuracy solvers orders magnitude shorter time.