Modified Homotopy Perturbation Transform Method: A Paradigm for Nonlinear Boundary Layer Problems
International Journal of Nonlinear Sciences and Numerical Simulation
This paper suggests a novel modified homotopy perturbation transform method (MHPTM) for a nonlinear boundary layer problem by suitable choice of an initial solution. The steady Navier–Stokes equations are reduced to nonlinear ordinary differential equations by using similarity variables. The governing nonlinear differential equations are solved by means of MHPTM. The equations are Laplace transformed and the nonlinear terms represented by He's polynomials. The series solution of the nonlinear boundary layer problem is obtained. For such a boundary layer problem, the second derivative at zero is an important point of function, so we have computed f″(0) and compared it with other results. An excellent agreement between the MHPTM and HPM is achieved. Such flow analysis is even not available yet for the hydrodynamic fluid. The series solution for MHD boundary layer problem with slip condition by means of MHPTM is yet not available in the literature.
homotopy perturbation transform method; boundary layer problem; slip condition; He's polynomials; series solution; Padé approximants
Khan, Yasir and Usman, Muhammad, "Modified Homotopy Perturbation Transform Method: A Paradigm for Nonlinear Boundary Layer Problems" (2014). Mathematics Faculty Publications. 1.