摘要:

AbstractA new numerical technique for investigating light waves guided by planar nonlinear dielectric films is presented. The method implements a multidomain spectral type approximation based on orthogonal algebraic polynomials, and makes possible to deal with nonperiodic boundary conditions and discontinuities of the data, overcoming the known deficiencies of the trigonometric polynomials. Results of preliminary numerical experiments for the solution of the nonlinear Schrödinger equation are presented. © 1994 John Wiley&Sons, In

ISSN:0749-159X    

DOI:10.1002/num.1690100603

出版商:John Wiley&Sons, Inc.    

年代:1994

数据来源: WILEY

摘要:

Abstractvon Rosenberg developed an explicit finite‐difference scheme for solution of the linear convection‐conduction partial differential equation in one space dimension. The method is stable and accurate when a dimensionless ratio of dispersion to convection is between zero and one. In this work, the von Rosenberg method was applied to a linear, one space dimensional set of coupled convection‐conduction equations. The system examined involves the change in temperature resulting from a fluid flowing through a stationary porous solid with heat transfer between the fluid and solid phases. The equations, which describe heat transfer in each phase, were solved simultaneously and, thus, the solution method was required to be implicit rather than explicit. It was observed that when the interphase convective heat‐transfer rate was small relative to the fluid velocity, an implicit solution of the von Rosenberg weighted equations provided a good solution, but when the interphase convective heat‐transfer rate was relatively large, a modified weighting on the equations provided a more accurate, stable solution. © 1994 John Wiley

ISSN:0749-159X    

DOI:10.1002/num.1690100604

出版商:John Wiley&Sons, Inc.    

年代:1994

数据来源: WILEY

摘要:

AbstractThe nonlinear Poisson‐Boltzmann equation is solved in the region between a sphere and a plane, which models the electrolyte solution interface between the tip and the substrate in a scanning tunneling microscope. A finite difference method is used with the domain transformed into bispherical coordinates. Picard iteration with relaxation is used to achieve convergence for this highly nonlinear problem. An adsorbed molecule on the substrate can also be modelled by a superposition of a perturbing potential in a small region of the plane. An approximate analytical solution using a superposition of individual solutions for plane, the adsorbed molecule, and the sphere is also attempted. Results for cases of different potential values on the boundary surfaces and different distances of the sphere from the plane are presented. The results of the numerical method, the approximate analytical method, as well as the previous solutions of the linearized equation are compared. © 1994 John Wiley&Sons, I

ISSN:0749-159X    

DOI:10.1002/num.1690100605

出版商:John Wiley&Sons, Inc.    

年代:1994

数据来源: WILEY

摘要:

AbstractAn Alternating Direction Implicit (ADI), Approximate Factorization (AF) scheme is presented here for the solution of the two‐dimensional elliptic partial differential equations, with control functions as source terms, used for grid generation. This scheme requires significantly less computational effort than a Successive Over Relaxation (SOR) scheme. The dependence of the choice of the acceleration parameter on the rate of convergence of the AF scheme has been studied. As an example, grids generated by this method are shown, along with a comparison of the convergence history for the present AF and SOR schemes. © 1994 John Wiley&Sons, I

ISSN:0749-159X    

DOI:10.1002/num.1690100606

出版商:John Wiley&Sons, Inc.    

年代:1994

数据来源: WILEY

摘要:

AbstractIn this article we deal with the solution in Ω ⊂R2of the quasi linear equation −Δu=f(x, y, u(x, y)) subject to mixed boundary data and representing Gauss' law in a semiconductor device, whereuandfare, respectively, the electrostatic potential and the space charge density after a suitable scaling. In the following we consider the associated variational problem of finding in a suitable subspace of H1(Ω) the minimum of the functional\documentclass{article}\pagestyle{empty}\begin{document}$ J(u)\, = \,\int {_\Omega } (\frac{1}{2}\left| {\nabla u\left| {^2 \, - \,{\cal F}(x,y,u)\,d\Omega,} \right.} \right. $\end{document}, where\documentclass{article}\pagestyle{empty}\begin{document}$ {\cal F}(x,y,u)\, = \,\int f (x,y,\xi)\,d\xi, $\end{document}and we prove existence and uniqueness of a weak solution according to the technique of Convex Analysis. The numerical study is then carried on by a piecewise linear finite element approximation, which is proved to converge in the H1‐norm to the exact solution of the variational problem; some numerical examples are also included. © 1994 John Wiley&

ISSN:0749-159X    

DOI:10.1002/num.1690100607

出版商:John Wiley&Sons, Inc.    

年代:1994

数据来源: WILEY

摘要:

AbstractFactors influencing the choice of ODE solver for the numerical solution of PDEs by the method of lines are investigated. The advection—diffusion equation is used to gain insight that is generalized to some classes of nonlinear PDEs. Numerical results for several nonlinear PDEs illustrate the theoretical developments. © 1994 John Wiley&Sons, I

ISSN:0749-159X    

DOI:10.1002/num.1690100608

出版商:John Wiley&Sons, Inc.    

年代:1994

数据来源: WILEY

摘要:

AbstractWe prove new pointwise estimates for the time‐continuous finite element discretization of a nonlinear Schrödinger equation. The analysis relies on the energy method. A superconvergent estimate of the error gradient is derived and we obtainL∞estimates via inverse inequalities. We emphasize the case of radial symmetry where the results improve on previously publishedL2estimates by allowing greater flexibility in the choice of spatial grid. Some numerical results are presented, which confirm our theoretical findings. © 1994 John Wiley&Sons

ISSN:0749-159X    

DOI:10.1002/num.1690100609

出版商:John Wiley&Sons, Inc.    

年代:1994

数据来源: WILEY

摘要:

AbstractWave propagation simulation requires a correct implementation of boundary conditions to avoid numerical instabilities. A boundary treatment based on characteristics, which includes as special cases more simple rheologies involving isotropy and elastic behavior, is applied to the anisotropic‐viscoelastic wave equation. The method introduces the boundary conditions by specifying the values of the incoming variables, which depend on the solution outside the model volume. The formulation ends up with a wave equation for the boundaries that implicitly includes the boundary conditions. The examples illustrate common problems in geophysical modeling, including free surface and nonreflecting conditions. © 1994 John Wiley&Sons, I

ISSN:0749-159X    

DOI:10.1002/num.1690100610

出版商:John Wiley&Sons, Inc.    

年代:1994

数据来源: WILEY

摘要:

AbstractWe study superconvergence of edge finite element approximations to the magnetostatic problem and to the time‐dependent Maxwell system. We show that in special discrete norms there is an increase of one power in the order of convergence of the finite element method compared to error estimates in standard Sobolev norms. Our results are restricted to an orthogonal grid inR3, but the grid may be nonuniform. © 1994 John Wiley&Sons, I

ISSN:0749-159X    

DOI:10.1002/num.1690100611

出版商:John Wiley&Sons, Inc.    

年代:1994

数据来源: WILEY

ISSN:0749-159X    

DOI:10.1002/num.1690100602

出版商:John Wiley&Sons, Inc.    

年代:1994

数据来源: WILEY