Approximate analytical solutions of reaction-diffusion equations with exponential source term: Homotopy perturbation method (HPM)
The authors apply the homotopy perturbation method to obtain approximate analytical solutions to the following problems: \[ {du\over dx}+\delta e^u= 0,\quad u(0)= 0, \] \[ {d^2u\over dx^2}+ {\ell\over x} {du\over dx}+\delta x^{-\beta} e^u= 0,\quad {du\over dx}(0)= 0,\;u(1)= 0, \] \[ {\partial u\over\partial t}= {\partial^2u\over\partial x^2}+\delta e^u= 0,\quad u(x,0)={1\over 2} x(1-x), \] \[ {\partial u\over\partial x} (0,t)\equiv 0,\quad u(1,t)\equiv 0. \]
scientific article; zbMATH DE number 5919231