Gauss Elimination and LU Decompositions of Matrices

2015 ◽  
pp. 81-102
Keyword(s):  
Gauss Elimination

scholarly journals Viscoelastic Fluid over a Stretching Sheet with Electromagnetic Effects and Nonuniform Heat Source/Sink

2010 ◽  
Vol 2010 ◽  
pp. 1-14 ◽  
Author(s):  
Kai-Long Hsiao
Keyword(s):  
Heat Transfer ◽  
Heat Source ◽  
Viscoelastic Fluid ◽  
Stretching Sheet ◽  
Numerical Solutions ◽  
Transfer Effects ◽  
Gauss Elimination ◽  
Heat Transfer Effects ◽  
Source Sink ◽  
Gauss Elimination Method

A magnetic hydrodynamic (MHD) of an incompressible viscoelastic fluid over a stretching sheet with electric and magnetic dissipation and nonuniform heat source/sink has been studied. The buoyant effect and the electric numberE1couple with magnetic parameterMto represent the dominance of the electric and magnetic effects, and adding the specific item of nonuniform heat source/sink is presented in governing equations which are the main contribution of this study. The similarity transformation, the finite-difference method, Newton method, and Gauss elimination method have been used to analyze the present problem. The numerical solutions of the flow velocity distributions, temperature profiles, and the important wall unknown values off''(0)andθ'(0)have been carried out. The parameter Pr,E1, orEccan increase the heat transfer effects, but the parameterMorA*may decrease the heat transfer effects.

Gauss elimination algorithms for mimd computers

1986 ◽  
pp. 247-254 ◽  
Author(s):  
M. Cosnard ◽  
M. Marrakchi ◽  
Y. Robert ◽  
D. Trystram
Keyword(s):  
Gauss Elimination

Gram-Schmidt Orthogonalization by Gauss Elimination

1991 ◽  
Vol 98 (6) ◽  
pp. 544-549 ◽  
Author(s):  
Lyle Pursell ◽  
S. Y. Trimble
Keyword(s):  
Gauss Elimination ◽  
Schmidt Orthogonalization

A numerical algorithm based on scale-3 Haar wavelets for fractional advection dispersion equation

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Sapna Pandit ◽  
R.C. Mittal
Keyword(s):  
Haar Wavelet ◽  
Haar Wavelets ◽  
System Control ◽  
Partial Differential ◽  
Content Type ◽  
Advection Dispersion ◽  
Novel Approach ◽  
Gauss Elimination ◽  
Time Variables ◽  
First Time

Purpose This paper aims to propose a novel approach based on uniform scale-3 Haar wavelets for unsteady state space fractional advection-dispersion partial differential equation which arises in complex network, fluid dynamics in porous media, biology, chemistry and biochemistry, electrode – electrolyte polarization, finance, system control, etc. Design/methodology/approach Scale-3 Haar wavelets are used to approximate the space and time variables. Scale-3 Haar wavelets converts the problems into linear system. After that Gauss elimination is used to find the wavelet coefficients. Findings A novel algorithm based on Haar wavelet for two-dimensional fractional partial differential equations is established. Error estimation has been derived by use of property of compactly supported orthonormality. The correctness and effectiveness of the theoretical arguments by numerical tests are confirmed. Originality/value Scale-3 Haar wavelets are used first time for these types of problems. Second, error analysis in new work in this direction.

Solution of the Immiscible Fluid Flow Simulation Equations

1969 ◽  
Vol 9 (02) ◽  
pp. 155-169 ◽  
Author(s):  
E.A. Breitenbach ◽  
D.H. Thurnau ◽  
H.K. Van Poolen
Keyword(s):  
Finite Difference ◽  
Numerical Solution ◽  
Difference Equations ◽  
Computing Time ◽  
Flow Simulation ◽  
Computational Technique ◽  
Immiscible Fluid ◽  
Finite Difference Equations ◽  
Gauss Elimination ◽  
Point Form

American Institute of Mining, Metallurgical and Petroleum Engineers, Inc. Abstract This paper presents the methods used to solve the finite difference equations which we developed in a companion paper (1). Various possible methods of solution are discussed. Experience has narrowed the numb of suitable numerical methods that are practical to three: Gauss elimination, successive practical to three: Gauss elimination, successive overrelaxation, and the iterative alternating direction implicit process. The final sections of the paper are devoted to a presentation of computational technique which are vital to actual use of each of the above-mentioned methods. FINITE DIFFERENCE EQUATIONS, THE MATRIX AND DEFINITIONS The final finite difference equation for pressure developed in Reference (1) is: pressure developed in Reference (1) is: ..........................................(1) All the terms are defined in the paper. Here, however, we have dropped the subscript denoting the pressure, p, as an oil pressure. Further breakdown requires definition of the numerical solution to be used. This paper describes the breakdown and solution processes most often used in the MUFFS program. Sufficient detail is given so that computer programming can be done. Contrary to popular opinion, economic simulation has been found to require the development of several solution methods, rather than relying on a single one. This requires that the computer subprogram for generating coefficients (A's and O's) be written as a distinct, separate entity to supply the coefficients in Equation (1). Furthermore, it is necessary to be able to obtain these coefficients automatically in column-by-column, row-by-raw, or point-by-point form, in any order required by a point-by-point form, in any order required by a numerical solution. Columns, rows, and points refer to the columns, rows, and points of the finite difference grid. A program that can generate coefficients in several forms is a simple but important concept, for it allows the easy insertion and modification of experimental methods. The computing inefficiencies that may be incurred within a general coefficient generator are small in comparison to the computing time saved by using the fastest of several solution techniques.

Integral Equation Approach for Computing Green’s Function on Doubly Connected Regions via the Generalized Neumann Kernel

2014 ◽  
Vol 71 (1) ◽  
Author(s):  
Siti Zulaiha Aspon ◽  
Ali Hassan Mohamed Murid ◽  
Mohamed M. S. Nasser ◽  
Hamisan Rahmat
Keyword(s):  
Integral Equation ◽  
Dirichlet Problem ◽  
Linear System ◽  
Green’S Function ◽  
Green's Function ◽  
Boundary Integral ◽  
Generalized Neumann Kernel ◽  
Integral Equation Approach ◽  
Gauss Elimination ◽  
Neumann Kernel

This research is about computing the Green’s function on doubly connected regions by using the method of boundary integral equation. The method depends on solving a Dirichlet problem. The Dirichlet problem is then solved using a uniquely solvable Fredholm integral equation on the boundary of the region. The kernel of this integral equation is the generalized Neumann kernel. The method for solving this integral equation is by using the Nystrӧm method with trapezoidal rule to discretize it to a linear system. The linear system is then solved by the Gauss elimination method. Mathematica plots of Green’s functions for several test regions are also presented.

Diagonalization of Quadratic Forms by Gauss Elimination

1966 ◽  
Vol 12 (5) ◽  
pp. 371-379 ◽  
Author(s):  
Charles S. Beightler ◽  
Douglass J. Wilde
Keyword(s):  
Quadratic Forms ◽  
Gauss Elimination
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