Generalized approximation method for heat radiation equations

• Published in: Applied mathematics and computation Vol. 212; no. 2; pp. 287 - 295
• Main Author: Khan, Rahmat Ali
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier Inc 15.06.2009; Elsevier
• Subjects: Exact sciences and technology; Generalized approximation; Heat transfer; Mathematical analysis; Mathematics; Numerical analysis; Numerical analysis. Scientific computation; Partial differential equations; Radiation equation; Sciences and techniques of general use; Upper and lower solutions; Upper and lower solutions; Radiation equation; Heat transfer; Generalized approximation; Perturbation method; Numerical analysis; Approximation; Heat equation; Applied mathematics; Homotopy; Nonlinear problems; Boundary condition
• ISSN: 0096-3003; 1873-5649
• DOI: 10.1016/j.amc.2009.02.028

Generalized approximation technique for the solution of heat transfer problem of the type y ″ ( x ) - ϵ y 4 ( x ) = 0 , x ∈ ( 0 , 1 ) subject to the boundary conditions y ′ ( 0 ) = 0 , y ( 1 ) = 1 is 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.