An efficient numerical method for solving linear and nonlinear partial differential equations by combining homotopy
analysis and transform method.
This shows that He's Homotopy
Pertubation method is an effective method for solving similar flow problems.
They performed a homotopy
deformation on successively refined discretization systems in order to obtain solutions on the finer level.
According to the homotopy
perturbation method, we assume that the solution of (10)-(11) can be written as
Method of Solution by the Homotopy
Perturbation Method (HPM) is a special case of the homotopy
analysis method (HAM) .
In the frame of the homotopy
method, we first construct such a continuous variation (or deformation) [phi] (x, t; q) that as q increases from 0 to 1, [phi] (x, t; q) varies from the initial approach [u.sub.0](x, t) to the solution u(x, t) of (3).
The fixed-point set is included as a subspace of the homotopy
fixed-point set, Fix(f/p) [??] h-Fix(f/p), by mapping to [~.x] to ([~.x],[alpha]) where [alpha] is the constant path at p([~.x]) = f([~.x]).
Section 2 introduces two parameters and constructs appropriate perturbations to the constraint functions to develop a non-interior point homotopy
path-following method for solving fixed-point problems with equality and inequality constraints.
According to HPLM, a homotopy
can be constructed as m(x, p) : R x [0,1] [right arrow] R such that it satisfies
The analytical solutions of TFPDE with proportional delay have been obtained by employing homotopy
perturbation method by Sakar et al.
The governing differential equations are transformed by the similarity transformations to two nonlinear ordinary differential equations, and then the resulting nonlinear ODEs are solved using the semi-analytical homotopy
perturbation method (HPM) for six types of nanoparticles: copper (Cu), alumina (Al2O3), titania (TiO2), copper oxide (CuO), silver (Ag) and silicon (SiO2) in the water based fluid with Pr = 6.2.