Control of error in the homotopy analysis of solutions to the Zakharov system with dissipation

    Authors

    K. Mallory;R. A. Van Gorder

    Comments

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    Abbreviated Journal Title

    Numer. Algorithms

    Keywords

    Zakharov system; Nonlinear partial differential equation; Control of; residual error; Time evolution auxiliary operator; NONLINEAR DIFFERENTIAL-EQUATIONS; VISCOUS-FLOW PROBLEMS; NON-NEWTONIAN; FLUIDS; EMDEN-FOWLER TYPE; ANALYTIC SOLUTION; SERIES SOLUTIONS; GENERAL-APPROACH; SOLITARY WAVES; BOUNDARY; DYNAMICS; Mathematics, Applied

    Abstract

    We apply the method of homotopy analysis to the Zakharov system with dissipation in order to obtain analytical solutions, treating the auxiliary linear operator as a time evolution operator. Evolving the approximate solutions in time, we construct approximate solutions which depend on the convergence control parameters. In the situation where solutions are strongly coupled, there will be multiple convergence control parameters. In such cases, we will pick the convergence control parameters to minimize a sum of squared residual errors. We explain the error minimization process in detail, and then demonstrate the method explicitly on several examples of the Zakharov system held subject to specific initial data. With this, we are able to efficiently obtain approximate analytical solutions to the Zakharov system of minimal residual error using approximations with relatively few terms.

    Journal Title

    Numerical Algorithms

    Volume

    64

    Issue/Number

    4

    Publication Date

    1-1-2013

    Document Type

    Article

    Language

    English

    First Page

    633

    Last Page

    657

    WOS Identifier

    WOS:000327859500003

    ISSN

    1017-1398

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