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  • Articles  (11)
  • Numerical Methods  (9)
  • petroleum
  • 2020-2023
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  • 1990-1994  (9)
  • 1970-1974  (2)
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  • Mathematics  (11)
  • Geosciences  (2)
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  • Articles  (11)
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  • Mathematics  (11)
  • Geosciences  (2)
  • 1
    Electronic Resource
    Electronic Resource
    Stability of some boundary value methods for the solution of initial value problems (1993)
    Springer
    BIT 33 (1993), S. 434-451 
    Details
    ISSN: 1572-9125
    Keywords: 34A50 ; 65L05 ; 65L20 ; Ordinary Differential Equations ; Initial Value Problems ; Numerical Methods ; Stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The stability properties of three particular boundary value methods (BVMs) for the solution of initial value problems are considered. Our attention is focused on the BVMs based on the midpoint rule, on the Simpson method and on an Adams method of order 3. We investigate their BV-stability regions by considering the scalar test problem and constant stepsize. The study of the conditioning of the coefficient matrix of the discrete problem is extended to the case of variable stepsize and block ODE problems. We also analyse an appropriate choice for the stepsize for stiff problems. Numerical tests are reported to evidentiate the effectiveness of the BVMs and the differences among the BVMs considered.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01990527
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  • 2
    Electronic Resource
    Electronic Resource
    A lithologic data-recording form for a computer-based well-data system (1972)
    Springer
    Mathematical geology 4 (1972), S. 61-72 
    Details
    ISSN: 1573-8868
    Keywords: data processing ; data recording ; data files ; lithology ; petroleum ; stratigraphy
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Well-data files maintained by petroleum companies and service companies are important sources of data for exploration geologists. To make these data readily accessible and useful for computer studies, three preliminary steps are necessary: (1) systematic data gathering and recording, (2) storage for ready retrieval, and (3) preparation of analysis programs. One important source of geologic data is lithologic descriptions of well cuttings and cores. The practical lithologic data-recording form described here is used routinely at the well site and in the laboratory. It is designed in an 80-column format and uses codes for lithologic characteristics, porosity, and hydrocarbon shows, and forms part of an integrated well-data file. This datarecording form has the advantages that descriptions are made according to a standardized format convenient to use at the well site, and the data are subsequently available in raw form relatively free from interpretive bias. A library of analysis and display programs can be assembled for utilization of the data.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02083194
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  • 3
    Electronic Resource
    Electronic Resource
    A piecewise exponential model for seismic well-logging data (1974)
    Springer
    Mathematical geology 6 (1974), S. 33-45 
    Details
    ISSN: 1573-8868
    Keywords: inversion of data ; mathematics ; numerical analysis ; regression analysis ; geophysics ; petroleum ; well logging
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Conventional methods of analyzing sonic log data do not always yield accurate information on each velocity segment of a well. It is shown here that the velocity-depth parameters and the sections of approximately constant velocity may be more precisely defined by using an exponential spline to model the data.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02111925
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  • 4
    Electronic Resource
    Electronic Resource
    Solution of the Navier-Stokes equations by the spectral-difference method (1994)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 10 (1994), S. 345-368 
    Details
    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The Jacobi polynomial collocation method is extended to two and three dimensions by superimposing the individual one-dimensional expansions. Two innovative ideas are introduced in this article. The first is the cornerless/edgeless computational grid, and the second is the modified compressibility method, which is an iterative pressure solver. To evaluate the new method's applicability in solving the Navier-Stokes equation, the lid-driven cavity flow problem was solved. Two configurations were considered, the square cavity and the rectangular cavity with an aspect ratio of 2. A comparison of the center-line velocity profiles from two- and three-dimensional simulations at a Reynolds number of 1000 is provided for each of the configurations. The center-line velocity comparisons showed good quantitative agreement with previous studies. © 1994 John Wiley & Sons, Inc.
    Additional Material: 19 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/num.1690100307
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  • 5
    Electronic Resource
    Electronic Resource
    A novel numerical technique to investigate nonlinear guided waves: Approximation of nonlinear Schrödinger equation by nonperiodic pseudospectral methods (1994)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 10 (1994), S. 667-675 
    Details
    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A 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, Inc.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/num.1690100603
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  • 6
    Electronic Resource
    Electronic Resource
    Sensitivity analysis of partial differential equations: A case for functional sensitivity (1991)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 7 (1991), S. 101-112 
    Details
    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Sensitivity analysis allows for analyzing the effects of parameter uncertainty. For functional parameters, the sensitivity of the system is described by the functional derivatives of the output variables with respect to the parameters. Approximation of each of the functional parameters by a finite number of scalars (via the finite element representation) allows one to use elementary sensitivity analysis. The functional sensitivities are easily approximated from elementary sensitivities and, being objective quantities, they allow one to evaluate the numerical quality of sensitivities. The grid density necessary for computing functional sensitivities may differ significantly from the grid required for the numerical solution of the governing equation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/num.1690070202
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  • 7
    Electronic Resource
    Electronic Resource
    Natural and postprocessed superconvergence in semilinear problems (1991)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 7 (1991), S. 245-259 
    Details
    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Superconvergence error estimates are established for a class of semilinear problems defined by a linear elliptic operator with a nonlinear forcing term. The analysis is for rectangular biquadratic elements, and we prove superconvergence of the derivative components along associated lines through the Gauss points. Derivative postprocessing formula and formulas for integrals are also considered and similar superconvergence estimates proven.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/num.1690070304
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  • 8
    Electronic Resource
    Electronic Resource
    Explicit block iterative method for the solution of the biharmonic equation (1993)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 9 (1993), S. 1-12 
    Details
    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We develop an iterative algorithm for the solution of a finite difference approximation of the biharmonic equation over a rectangular region by using the explicit block iterative method, i.e., box over relaxation scheme. The 4- and 9-point explicit blocks were considered and performance results for the two algorithms are presented.© 1993 John Wiley & Sons, Inc.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/num.1690090102
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  • 9
    Electronic Resource
    Electronic Resource
    Domain-imbedding alternating direction method for linear elliptic equations on irregular regions using collocation (1993)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 9 (1993), S. 93-106 
    Details
    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A new method is presented for solving elliptic partial differential equations over two-dimensional irregular regions. The scheme imbeds the irregular region in a rectangle, and then uses an alternating direction iteration to solve the resulting system of linear equations. Collocation with cubic Hermite splines is used for discretization. The method is shown to be equivalent to a multiboundary alternating direction method. A theory of convergence for a simplified case is given, details of implementation are discussed, and two numerical illustrations are presented. © 1993 John Wiley & Sons, Inc.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/num.1690090109
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  • 10
    Electronic Resource
    Electronic Resource
    On parallel algorithms for semidiscretized parabolic partial differential equations based on subdiagonal Padé approximations (1993)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 9 (1993), S. 107-116 
    Details
    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: It is well known that methods for solving semidiscretized parabolic partial differential equations based on the second-order diagonal [1/1] Padé approximation (the Crank-Nicolson or trapezoidal method) can produce poor numerical results when a time discretization is imposed with steps that are “too large” relative to the spatial discretization. A monotonicity property is established for all diagonal Padé approximants from which it is shown that corresponding higher-order methods suffer a similar time step restriction as the [1/1] Padé. Next, various high-order methods based on subdiagonal Padé approximations are presented which, through a partial fraction expansion, are no more complicated to implement than the first-order implicit Euler method based on the [0/1] Padé approximation; moreover, the resulting algorithms are free of a time step restriction intrinsic to those based on diagonal Padé approximations. Numerical results confirm this when various test problems from the literature are implemented on a Multiple Instruction Multiple Data (MIMD) machine such as an Alliant FX/8. © 1993 John Wiley & Sons, Inc.
    Additional Material: 3 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/num.1690090202
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