Method for constructing analytical solutions to the Dym initial value problem

• Published in: Applied mathematics and computation Vol. 226; pp. 67 - 82
• Main Authors: Mallory, Kristina, Van Gorder, Robert A.
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 01.01.2014
• Subjects: Analytical solution; Approximation; Auxiliary linear operator; Convergence; Dym equation; Evolution; Initial value problems; Linear operators; Mathematical analysis; Mathematical models; Nonlinear PDE; Optimal control of error; Optimal homotopy analysis method; Optimization; Dym equation; Auxiliary linear operator; Nonlinear PDE; Optimal homotopy analysis method; Analytical solution; Optimal control of error

We obtain approximate solutions to the Dym equation, and associated initial value problem, for general initial data by way of an optimal homotopy analysis method. By varying the auxiliary linear operator, thereby varying the time evolution of approximate solutions, we perform two independent homotop...