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  • 1
    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
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  • 2
    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
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  • 3
    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
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  • 4
    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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  • 5
    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
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  • 6
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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
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  • 7
    Publication Date: 2019-07-12
    Description: Black carbon, light-absorbing organic carbon (often called brown carbon) and mineral dust are the major light-absorbing aerosols. Currently the sources and formation of brown carbon aerosol in particular are not well understood. In this study we estimated globally the amount of light absorbing organic carbon and black carbon from AERONET measurements. We find that the columnar absorbing organic carbon (brown carbon) levels in biomass burning regions of South-America and Africa are relatively high (about 15-20 magnesium per square meters during biomass burning season), while the concentrations are significantly lower in urban areas in US and Europe. However, we estimated significant absorbing organic carbon amounts from the data of megacities of newly industrialized countries, particularly in India and China, showing also clear seasonality with peak values up to 30-35 magnesium per square meters during the coldest season, likely caused by the coal and biofuel burning used for heating. We also compared our retrievals with the modeled organic carbon by global Oslo CTM for several sites. Model values are higher in biomass burning regions than AERONET-based retrievals, while opposite is true in urban areas in India and China.
    Keywords: Earth Resources and Remote Sensing
    Type: NF1676L-11204
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