A hybrid perturbation-Galerkin technique for partial differential equations
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A hybrid perturbation-Galerkin technique for partial differential equations

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Published by NASA Langley Research Center in Hampton, Va .
Written in English


  • Perturbation (Mathematics),
  • Differential equations, Partial.,
  • Galerkin methods.

Book details:

Edition Notes

Other titlesHybrid perturbation Galerkin technique for partial differential equations.
StatementJames F. Geer, Carl M. Anderson.
SeriesICASE report -- no. 90-57., NASA contractor report -- 182085., NASA contractor report -- NASA CR-182085.
ContributionsAndersen, Carl M. 1930-, Institute for Computer Applications in Science and Engineering., Langley Research Center.
The Physical Object
Pagination1 v.
ID Numbers
Open LibraryOL18063793M

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A two-step hybrid perturbation-Galerkin technique for improving the usefulness of perturbation solutions to partial differential equations which contain a parameter is presented and : James F. Geer and Carl M. Anderson.   The Hybrid-Galerkin perturbation method is then applied to each of the perturbation solutions derived. In each case the resultant Hybrid-Galerkin solution is compared to its corresponding perturbation solution for various values of ε and Ω. Both methods are also compared to a fourth-order Runge-Kutta solution of the given differential by: 4. A two-step hybrid perturbation-Galerkin method for the solution of a variety of differential equations-type problems is found to give better results when multiple perturbation expansions are by:   A two-step hybrid technique, which combines perturbation methods based on the parameter ρ = Δ t ∕ (Δ x) 2 with the Galerkin method, provides a systematic way to develop new finite difference methods, referred to as hybrid equations.

A perturbation solution is obtained for both the interfacial position and the velocity potential, and then improved using a Galerkin technique. The distortion of the interface by the source is found to be localized and nonmonotonic, and weakly modified by surface tension. differential equations away from the analytical computation of solutions and toward both their numerical analysis and the qualitative theory. This book provides an introduction to the basic properties of partial dif-ferential equations (PDEs) and to the techniques that have proved useful in analyzing them.   This paper proposes a symmetry–iteration hybrid algorithm for solving boundary value problems for partial differential equations. First, the multi-parameter symmetry is used to reduce the problem studied to a simpler initial value problem for ordinary differential equations. The aim of this is to introduce and motivate partial di erential equations (PDE). The section also places the scope of studies in APM within the vast universe of mathematics. What is a PDE? A partial di erential equation (PDE) is an equation involving partial deriva-tives. This is not so informative so let’s break it down a bit.

Get this from a library! A hybrid perturbation-Galerkin technique for partial differential equations. [James F Geer; Carl M Andersen; Institute for Computer Applications in Science and Engineering.; Langley Research Center.]. This is a linear partial differential equation of first order for µ: Mµy −Nµx = µ(Nx −My). 5. Two C1-functions u(x,y) and v(x,y) are said to be functionally dependent if det µ ux uy vx vy = 0, which is a linear partial differential equation of first order for u if v is a given C1-function. A large class of solutions is given by. Asymptotic Analysis and the Numerical Solution of Partial Differential Equations book. using from N = toN = terms. = the radius of convergence, R, of the series expansion. that the hybrid method might be a useful tool for the of Andersen and J. F. Geer, Investigating a hybrid perturbation Galerkin technique NASA Langley,!CASE Report No. With a physically prototyped analog accelerator, we use this hybrid analog-digital method to solve the two-dimensional viscous Burgers' equation an important and representative PDE. For large grid sizes and nonlinear problem parameters, the hybrid method reduces the solution time by ×, and reduces energy consumption by ×, compared.