Application of homotopy-perturbation and variational iteration methods to nonlinear heat transfer and porous media equations

摘要: Perturbation methods depend on a small parameter which is difficult to be found for real-life nonlinear problems. To overcome this shortcoming, two new but powerful analytical are introduced solve heat transfer problems in article; one He's variational iteration method (VIM) and the other homotopy-perturbation (HPM). The VIM construct correction functionals using general Lagrange multipliers identified optimally via theory, initial approximations can freely chosen with unknown constants. HPM deforms problem into simple easily solved. Nonlinear convective-radiative cooling equation, equation (porous media equation) cubic nonlinearity used as examples illustrate solution procedures. Comparison of applied exact solutions reveals that both tremendously effective.