Last edited by Gataur
Wednesday, August 5, 2020 | History

3 edition of A hybrid perturbation-Galerkin technique for partial differential equations found in the catalog.

A hybrid perturbation-Galerkin technique for partial differential equations

# A hybrid perturbation-Galerkin technique for partial differential equations

Written in English

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

• Edition Notes

The Physical Object ID Numbers Other titles Hybrid perturbation Galerkin technique for partial differential equations. Statement James F. Geer, Carl M. Anderson. Series ICASE report -- no. 90-57., NASA contractor report -- 182085., NASA contractor report -- NASA CR-182085. Contributions Andersen, Carl M. 1930-, Institute for Computer Applications in Science and Engineering., Langley Research Center. Format Microform Pagination 1 v. Open Library OL18063793M

A hybrid perturbation-Galerkin technique for partial differential equations / James Geer and Carl M. Andersen --On the equations of physical oceanography / A. Louise Perkins --Transonics and asymptotics / L. Pamela Cook --Evolution to detonation in a nonuniformly heated reactive medium / A.K. Kapila and J.W. Dold --Surface evolution equations.   A hybrid reduced-order modeling technique for nonlinear structural dynamic simulation. 30 October | Numerical Methods for Partial Differential Equations, Vol. 31, No. 2 A Hybrid Perturbation Galerkin Technique with Applications to Slender Body Theory.

A two-step hybrid perturbation-Galerkin technique for improving the usefulness of per-turbation solutions to partial differential equations which contain a parameter is presented and discussed. In the first step of the method, the leading terms in the asymptotic expan-.   "For he who knows not mathematics cannot know any other sciences; what is more, he cannot discover his own ignorance or find its proper remedies. " [Opus Majus] Roger Bacon () The material presented in these monographs is the outcome of the author's long-standing interest in the analytical modelling of problems in mechanics by appeal to the theory of partial differential equations.

Partial Diﬀerential Equations in Physics and Engineering 29 Solution of the One Dimensional Wave Equation: The Method of Separation of Variables 31 D’Alembert’s Method 35 The One Dimensional Heat Equation 41 Heat Conduction in Bars: Varying the Boundary Conditions 43 The Two Dimensional Wave and Heat Equations With this notation, we are now ready to deﬁne a partial diﬀerential equation. A partial diﬀerential equation is an equation involving a function u of several variables and its partial derivatives. The order of the partial diﬀerential equation is the order of the highest-order derivative that appears in the equation. Example 3.

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### A hybrid perturbation-Galerkin technique for partial differential equations Download PDF EPUB FB2

A two-step hybrid perturbation Galerkin technique for solving a variety of applied mathematics problems involving a small parameter is presented.

The first step consists of using a regular or singular perturbation method to determine the asymptotic expansion of the solution in Cited by:   A broad treatment of important partial differential equations, particularly emphasizing the analytical techniques.

In each chapter the author raises various questions concerning the particular equations discussed, treats different methods for tackling these equations, gives applications and examples, and concludes with a list of proposed problems and a relevant by: 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). 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.

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. "The book is concerned with singular perturbation phenomena for ordinary and partial differential equations.

Instead of presenting general theory, the author shows how various perturbation techniques work in concrete examples Applications are quite numerous and include fluid dynamics, solid mechanics, and plasma physicsReviews: 2.

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.

In this paper, we propose an efficient alternating direction implicit (ADI) Galerkin method for solving the time-fractional partial differential equation with damping, where the fractional derivative is in the sense of Caputo with order in (1, 2) $(1,2)$.

The presented numerical scheme is based on the L2- 1 σ $1_{\\sigma}$ method in time and the Galerkin finite element method in space. Take an in-depth look at equity hybrid derivatives. Written by the quantitative research team of Deutsche Bank, the world leader in innovative equity derivative transactions, this book presents leading-edge thinking in modeling, valuing, and hedging for this market, which is increasingly used for investment by hedge funds.

In mathematics, a partial differential equation (PDE) is an equation which imposes relations between the various partial derivatives of a multivariable function. The function is often thought of as an "unknown" to be solved for, similarly to how x is thought of as an unknown number, to be solved for, in an algebraic equation like x 2 − 3x + 2 = 0.

A two-step hybrid analysis technique, which combines perturbation techniques with the Galerkin method, has been presented and discussed by the authors.

It was applied to some singular perturbation problems in slender body theory, as well as to several classes of. A student who reads this book and works many of the exercises will have a sound knowledge for a second course in partial differential equations or for courses in advanced engineering and science.

Two additional chapters include short introductions to applications of PDEs in biology and a new chapter to the computation of solutions. Take an in-depth look at equity hybrid derivatives.

Written by the quantitative research team of Deutsche Bank, the world leader in innovative equity derivative transactions, this book presents leading-edge thinking in modeling, valuing, and hedging for this market, which is increasingly used for investment by hedge funds.

You'll gain a balanced, integrated presentation of theory and practice 5/5(1).Partial Diﬀerential Equations Igor Yanovsky, 12 Weak Solutions for Quasilinear Equations Conservation Laws and Jump Conditions Consider shocks for an equation u t +f(u) x =0, () where f is a smooth function ofu.

If we integrate () with respect to x for a ≤ x ≤ b.