On the choice of auxiliary linear operator in the optimal homotopy analysis of the Cahn-Hilliard initial value problem
Abbreviated Journal Title
Cahn-Hilliard equation; Homotopy analysis method; Auxiliary linear; operator; Convergence control parameter; NONLINEAR DIFFERENTIAL-EQUATIONS; VISCOUS-FLOW PROBLEMS; NON-NEWTONIAN; FLUIDS; EMDEN-FOWLER TYPE; ANALYTIC SOLUTION; SERIES SOLUTIONS; GENERAL-APPROACH; FREE-ENERGY; WAVES; Mathematics, Applied
Analytical solutions for the Cahn-Hilliard initial value problem are obtained through an application of the homotopy analysis method. While there exist numerical results in the literature for the Cahn-Hilliard equation, a nonlinear partial differential equation, the present results are completely analytical. In order to obtain accurate approximate analytical solutions, we consider multiple auxiliary linear operators, in order to find the best operator which permits accuracy after relatively few terms are calculated. We also select the convergence control parameter optimally, through the construction of an optimal control problem for the minimization of the accumulated L-2-norm of the residual errors. In this way, we obtain optimal homotopy analysis solutions for this complicated nonlinear initial value problem. A variety of initial conditions are selected, in order to fully demonstrate the range of solutions possible.
"On the choice of auxiliary linear operator in the optimal homotopy analysis of the Cahn-Hilliard initial value problem" (2014). Faculty Bibliography 2010s. 5042.