摘要:

AbstractThe Petrov‐Galerkin projection method is outlined for the solution of the linear elliptic equationLu=fwith homogeneous boundary conditions. By choosing appropriate finite dimensional trial and test spaces, the methods of weighted residuals, collocation, andH1Galerkin can be interpreted within the Petrov‐Galerkin projection method framework.The important question of how best to choose the trial and test functions to suit a particular type of problem is then discussed. Objective criteria associated with the matrix which governs the Petrov‐Galerkin numerical process are pro

ISSN:0170-4214    

DOI:10.1002/mma.1670010102

出版商:John Wiley&Sons, Ltd    

年代:1979

数据来源: WILEY

摘要:

AbstractWe describe in this paper a finite element method for the solution of viscous incompressible flow problems which incorporates an approximate form of the incompressibility condition automatically into the finite element basis. Several examples of such finite elements are presented and applied to a simple test problem.

ISSN:0170-4214    

DOI:10.1002/mma.1670010103

出版商:John Wiley&Sons, Ltd    

年代:1979

数据来源: WILEY

摘要:

AbstractSolutions to the backwards heat equation are approximated by solutions of a pseudo‐heat equation. Solutions to this modified equation are constructed by means of a fundamental solution and potential theory, and it is shown that the fundamental solution can be approximated by various expansions in special function

ISSN:0170-4214    

DOI:10.1002/mma.1670010104

出版商:John Wiley&Sons, Ltd    

年代:1979

数据来源: WILEY

摘要:

AbstractIn this paper we consider a free boundary problem of general type for the heat equation in one space dimension. We formulate this problem as an optimal control problem and derive necessary conditions for a solution of it. In order to compute a solution of the control problem, we apply the projection‐gradient‐method. Simple numerical examples illustrate the resu

ISSN:0170-4214    

DOI:10.1002/mma.1670010105

出版商:John Wiley&Sons, Ltd    

年代:1979

数据来源: WILEY

摘要:

AbstractThe existence of periodic solutions of general first order nonlinear difference‐differential equations is shown using an appropriate cone of initial data and an asymptotic fixed point theore

ISSN:0170-4214    

DOI:10.1002/mma.1670010106

出版商:John Wiley&Sons, Ltd    

年代:1979

数据来源: WILEY

摘要:

AbstractPulse mode sonar operation is analyzed under the assumption that the scattering object Γ lies in the far fields of both the transmitter and the receiver. It is shown that, in this approximation, the sonar signal is a plane waves(x· θ0–t) near Γ, where θ0is a unit vector directed from the transmitter toward Γ, and similarly the echo is a plane wavee(x· θ –t) near the receiver, where θ is a unit vector directed from Γ toward the receiver. Moreover, if Γ is stationary with respect to the sonar system then it is shown thatwhere š(ω) is the Fourier transform ofS(τ) andT+(ωθ,ωθ0) is the scattering amplitude in the direction θ due to the scattering by Γ of a time‐harmonic plane wave with frequence ω and propagation direction θ0. A generalization of this relation is de

ISSN:0170-4214    

DOI:10.1002/mma.1670010107

出版商:John Wiley&Sons, Ltd    

年代:1979

数据来源: WILEY

摘要:

AbstractThe treatment of boundary value problems for Helmholtz equation and for the time harmonic Maxwell's equations by boundary integral equations leads to integral equations of the second kind which are uniquely solvable for small positive frequencies λ. However, the integral equations obtained in the limiting case λ = 0 which are related to boundary value problems of potential theory in general are not uniquely solvable since the corresponding boundary value problems are not. By first considering in a general setting of a Banach spaceXthe limiting behaviour of solutions ϕλto the equation ϕλ– K λ ϕ λ =fλ as λ → 0 where {Kλ:X→X, λ ∈ (0,α)}, α>0, denotes a family of compact linear operators such thatI‐Kλ(Iidentity) is bijective for λ∈(0,α) whilstI‐K0is not and ‖Kλ–K0‖ →, 0, ‖fλ–f0‖ → 0, λ → 0, and then applying the results to the boundary integral operators, the limiting behaviour of the integral equations is considered. Thus, the results obtained by Mac Camey for the Helmholtz equation are extended to the case of non‐connected boundaries and Werner's results on the integral equations for the Maxwell's equations are

ISSN:0170-4214    

DOI:10.1002/mma.1670010108

出版商:John Wiley&Sons, Ltd    

年代:1979

数据来源: WILEY

摘要:

AbstractThe interior initial‐boundary value problem for Maxwell's equations is considered for certain homogeneous boundary conditions and currents which satisfy corresponding compatibility conditions. Under the assumption that a solution exists, it is shown by means of suitable normed spaces that the sequence of discrete solutions obtained from the horizontal line method converges discretely to this solution. A priori estimations are given both for the discrete solutions and the solution of the given proble

ISSN:0170-4214    

DOI:10.1002/mma.1670010109

出版商:John Wiley&Sons, Ltd    

年代:1979

数据来源: WILEY

摘要:

AbstractLetAbe a selfadjoint uniformly elliptic differential operator. Let the underlying domain be bounded. Eigenvalue problems can be solved then, and an arbitrary square integrable function may be developed in a Fourier series relative to the eigenfunctions. In general elliptic differential operators have a continuous spectrum, if the underlying domain is unbounded. In this case the spectral theorem provides a representation of a given function by an integral transformation. The spectral projector can be calculated, if the outgoing and incoming solutions are known (radiation condition). Thus integral transformations may be derived very easily. Four examples will be given: the Fourier sine transform, the Lebedev transform, the transformation belonging to the Dirichlet problem of the plate equation and, finally, the Fourier transformation.

ISSN:0170-4214    

DOI:10.1002/mma.1670010110

出版商:John Wiley&Sons, Ltd    

年代:1979

数据来源: WILEY

ISSN:0170-4214    

DOI:10.1002/mma.1670010101

出版商:John Wiley&Sons, Ltd    

年代:1979

数据来源: WILEY