New numerical methods for the photoelastic technique with high accuracy

2012 ◽  
Vol 112 (8) ◽  
pp. 083111 ◽  
Author(s):  
Cristina Almeida Magalhaes ◽  
Pedro Americo Almeida Magalhaes
Keyword(s):  
Numerical Methods ◽  
High Accuracy

High-accuracy numerical methods for a parabolic system in air pollution modeling

2019 ◽  
Vol 32 (10) ◽  
pp. 6025-6040
Author(s):  
Venelin Todorov ◽  
Juri Kandilarov ◽  
Ivan Dimov ◽  
Luben Vulkov
Keyword(s):  
Air Pollution ◽  
Numerical Methods ◽  
Parabolic System ◽  
High Accuracy ◽  
Air Pollution Modeling ◽  
Pollution Modeling

scholarly journals High Accuracy Numerical Methods for Thermally Perfect Gas Flows with Chemistry

1997 ◽  
Vol 132 (2) ◽  
pp. 175-190 ◽  
Author(s):  
Ronald P. Fedkiw ◽  
Barry Merriman ◽  
Stanley Osher
Keyword(s):  
Numerical Methods ◽  
High Accuracy ◽  
Gas Flows ◽  
Perfect Gas

Fast and High Accuracy Numerical Methods for the Solution of Nonlinear Klein–Gordon Equations

2011 ◽  
Vol 66 (12) ◽  
pp. 735-744 ◽  
Author(s):  
Akbar Mohebbi ◽  
Zohreh Asgari ◽  
Alimardan Shahrezaee
Keyword(s):  
Numerical Methods ◽  
High Efficiency ◽  
High Accuracy ◽  
Processing Unit ◽  
Conservation Of Energy ◽  
One Dimensional ◽  
Central Processing ◽  
Time Stepping ◽  
Klein Gordon ◽  
The One

In this work we propose fast and high accuracy numerical methods for the solution of the one dimensional nonlinear Klein-Gordon (KG) equations. These methods are based on applying fourth order time-stepping schemes in combination with discrete Fourier transform to numerically solve the KG equations. After transforming each equation to a system of ordinary differential equations, the linear operator is not diagonal, but we can implement the methods such as for the diagonal case which reduces the time in the central processing unit (CPU). In addition, the conservation of energy in KG equations is investigated. Numerical results obtained from solving several problems possessing periodic, single, and breather-soliton waves show the high efficiency and accuracy of the mentioned methods.

High accuracy numerical methods for the Gardner–Ostrovsky equation

2014 ◽  
Vol 240 ◽  
pp. 140-148 ◽  
Author(s):  
M.A. Obregon ◽  
E. Sanmiguel-Rojas ◽  
R. Fernandez-Feria
Keyword(s):  
Numerical Methods ◽  
High Accuracy ◽  
Ostrovsky Equation

scholarly journals High accuracy mantle convection simulation through modern numerical methods – II: realistic models and problems

2017 ◽  
Vol 210 (2) ◽  
pp. 833-851 ◽  
Author(s):  
Timo Heister ◽  
Juliane Dannberg ◽  
Rene Gassmöller ◽  
Wolfgang Bangerth
Keyword(s):  
Numerical Methods ◽  
Mantle Convection ◽  
High Accuracy

scholarly journals High accuracy mantle convection simulation through modern numerical methods

2012 ◽  
Vol 191 (1) ◽  
pp. 12-29 ◽  
Author(s):  
Martin Kronbichler ◽  
Timo Heister ◽  
Wolfgang Bangerth
Keyword(s):  
Numerical Methods ◽  
Mantle Convection ◽  
High Accuracy

scholarly journals Calculation of aberration coefficients for a cylindrical mirror

2021 ◽  
Vol 31 (1) ◽  
Author(s):  
S. I. Shevchenko ◽  
Keyword(s):  
Numerical Methods ◽  
Fourth Order ◽  
Arbitrary Order ◽  
Azimuthal Angle ◽  
Arbitrary Point ◽  
High Accuracy ◽  
Arbitrary Angle ◽  
Cylindrical Mirror

Angular аberration coefficients for a cylindrical mirror up to the fourth order in the vicinity of the azimuthal angle φ0 = 0 and in the vicinity of an arbitrary angle ϑ0 value are analytically obtained. A method is developed for calculating aberration coefficients of arbitrary order and in the vicinity of an arbitrary point based on the results of calculating several trajectories. Analytical and numerical methods for calculating aberration coefficients up to the fourth order are productive in the vicinity of the point (φ0 = 0, ϑ0) that coincide with high accuracy.

EXPLICIT NUMEROV TYPE METHODS FOR SECOND ORDER IVPs WITH OSCILLATING SOLUTIONS

2001 ◽  
Vol 12 (05) ◽  
pp. 657-666 ◽  
Author(s):  
G. PAPAGEORGIOU ◽  
CH. TSITOURAS ◽  
I. TH. FAMELIS
Keyword(s):  
Numerical Methods ◽  
Taylor Expansion ◽  
High Accuracy ◽  
Order Conditions ◽  
Numerical Results ◽  
Phase Lag ◽  
New Approach ◽  
New Methods ◽  
Oscillating Solutions ◽  
Algebraic Order

New explicit hybrid Numerov type methods are presented in this paper. These efficient methods are constructed using a new approach, where we do not need the use of the intermediate high accuracy interpolatory nodes, since only the Taylor expansion of the internal points is needed. The methods share sixth algebraic order at a cost of five stages per step while their phase-lag order is 14 and partly satisfy the dissipation order conditions. It has be seen that the property of phase-lag is more important than the nonempty interval in constructing numerical methods for the solution of Schrödinger equation and related problems.1–3 Numerical results over some well known problems in physics and mechanics indicate the superiority of the new methods.

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