Generalized approximation method for heat radiation equations

Generalized approximation technique for the solution of heat transfer problem of the typey″(x)-ϵy4(x)=0,x∈(0,1)subject to the boundary conditionsy′(0)=0,y(1)=1is developed. The results obtained by the generalized approximation method (GAM) are compared with the results obtained by the homotopy perturbation method (HPM) and the perturbation method (PM). For very small ϵ, both HPM and PM yield good approximation while for a bit larger value of ϵ, both the methods produce bad results. However, the GAM yields good results for any value of ϵ. Moreover, the GAM generates a sequence of solutions of linear problems that converges monotonically and quadratically to solution of the original nonlinear problem.