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  • NUMERICAL ANALYSIS  (6)
  • torsional surface waves  (2)
  • 1
    Electronic Resource
    Electronic Resource
    New York, NY [u.a.] : Wiley-Blackwell
    International Journal for Numerical and Analytical Methods in Geomechanics 20 (1996), S. 287-294 
    ISSN: 0363-9061
    Keywords: torsional surface waves ; propagation ; hoterogeneous half-space ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Notes: The paper discusses the propagation of torsional surface wave in a homogeneous substratum over a half-space with linearly varying rigidity and density. The study reveals that under assumed conditions, a torsional surface wave propagates in the medium. The velocities of torsional surface waves have been calculated numerically and are presented in a number of graphs. It is also observed that for a stratum over a homogeneous half-space, the velocity of torsional surface waves coincides with that of Love waves. For a non-homogeneous half-space it is observed that the velocity of torsional surface waves is always higher than that of Love waves propagated in a homogeneous layer over a homogeneous half-space. An attempt is also made to assess the possible propagation of torsional surface waves in a half-space with linearly varying rigidity and density, lacking a superficial layer. It is concluded that such a half-space allows two solutions for torsional waves while a homogeneous half-space has one.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    New York, NY [u.a.] : Wiley-Blackwell
    International Journal for Numerical and Analytical Methods in Geomechanics 20 (1996), S. 209-213 
    ISSN: 0363-9061
    Keywords: torsional surface waves ; geophysical prospecting ; earthquake damage ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Notes: It is well known that an elastic homogeneous half-space does not allow torsional surface waves to propagate. The present paper attempts to find out the possibility of propagation of such waves in a viscoelastic half-space. The study reveals that although the homogeneous elastic half-space does not allow torsional surface waves to propagate, a viscoelastic half-space does so. The wave is damped due to the viscoelastic parameter. It has also been found that as the viscoelastic parameter decreases, the medium becomes elastic and the torsional surface waves ceases to propagate.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
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  • 3
    Publication Date: 2011-08-18
    Description: An explicit finite difference scheme consisting of a predictor and a corrector has been developed and applied to solve some hyperbolic partial differential equations (PDEs). The corrector is a convex-type function which is applied at each time level and at each mesh point. It consists of a parameter which may be estimated such that for larger time steps the algorithm should remain stable and generate a fast speed of convergence to the steady-state solution. Some examples have been given.
    Keywords: NUMERICAL ANALYSIS
    Type: Computers and Mathematics with Applications (ISSN 0097-4943); 9; 3, 19; 1983
    Format: text
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  • 4
    Publication Date: 2016-06-07
    Description: Finite difference solutions of nonlinear partial differential equations require discretizations and consequently grid errors are generated. These errors strongly affect stability and convergence properties of difference models. Previously such errors were analyzed by linearizing the difference equations for solutions. Properties of mappings of decadence were used to analyze nonlinear instabilities. Such an analysis is directly affected by initial/boundary conditions. An algorithm was developed, applied to nonlinear Burgers equations, and verified computationally. A preliminary test shows that Navier-Stokes equations may be treated similarly.
    Keywords: NUMERICAL ANALYSIS
    Type: NASA. Langley Research Center Numerical Grid Generation Tech.; p 221-230
    Format: application/pdf
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  • 5
    Publication Date: 2019-06-28
    Description: Numerical modeling of D-mappings was studied and applied to solving nonlinear stiff systems. These mappings were locally linearized for convergence analysis, and some applications were made to chemical kinetics. The technique avoids using multistep implicit codes that require inversion of Jacobian matrices, but depends on the Jacobians for its convergence analysis.
    Keywords: NUMERICAL ANALYSIS
    Type: NASA-TM-84332 , A-9256 , NAS 1.15:84332
    Format: application/pdf
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  • 6
    Publication Date: 2019-06-28
    Description: Numerical solution of nonlinear stiff initial value problems by a perturbed functional iterative scheme is discussed. The algorithm does not fully linearize the system and requires only the diagonal terms of the Jacobian. Some examples related to chemical kinetics are presented.
    Keywords: NUMERICAL ANALYSIS
    Type: NASA-TM-84234 , NAS 1.15:84234
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  • 7
    Publication Date: 2019-06-28
    Description: Forward Euler's explicit, finite-difference formula of extrapolation, is used as a predictor and a convex formula as a corrector to integrate differential equations numerically. An application has been made to Burger's equation.
    Keywords: NUMERICAL ANALYSIS
    Type: NASA-TM-84402 , A-9475 , NAS 1.15:84402
    Format: application/pdf
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  • 8
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    In:  Other Sources
    Publication Date: 2019-07-13
    Description: A perturbed functional iteration has been developed to solve nonlinear systems. It adds at each iteration level, unique perturbation parameters to nonlinear Gauss-Seidel iterates which enhances its convergence properties. As convergence is approached these parameters are damped out. Local linearization along the diagonal has been used to compute these parameters. The method requires no computation of Jacobian or factorization of matrices. Analysis of convergence depends on properties of certain contraction-type mappings, known as D-mappings. In this article, application of this method to solve an implicit finite difference approximation of Euler's equation is studied. Some representative results for the well known shock tube problem and compressible flows in a nozzle are given.
    Keywords: NUMERICAL ANALYSIS
    Type: Large-scale computations in fluid mechanics; Jun 27, 1983 - Jul 08, 1983; La Jolla, CA
    Format: text
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