Analytic approximation of solutions of parabolic partial differential equations with variable coefficients

Vladislav V. Kravchenko, Josafath A. Otero, Sergii M. Torba

A complete family of solutions for the one-dimensional reaction-diffusion equation \[ u_{xx}(x,t)-q(x)u(x,t) = u_t(x,t) \] with a coefficient $q$ depending on $x$ is constructed. T…