New explicit group iterative methods in the solution of two dimensional hyperbolic equations

2012 ◽  
Vol 231 (20) ◽  
pp. 6953-6968 ◽  
Author(s):  
Norhashidah Hj. Mohd. Ali ◽  
Lee Ming Kew
Keyword(s):  
Iterative Methods ◽  
Hyperbolic Equations ◽  
Two Dimensional

scholarly journals Weighted Essentially Nonoscillatory Method for Two-Dimensional Population Balance Equations in Crystallization

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Chunlei Ruan ◽  
Kunfeng Liang ◽  
Xianjie Chang ◽  
Ling Zhang
Keyword(s):  
Crystal Size ◽  
Hyperbolic Equations ◽  
Population Balance ◽  
Numerical Dispersion ◽  
Two Dimensional ◽  
Governing Equations ◽  
Balance Equations ◽  
Population Balance Equations ◽  
Weighted Essentially Nonoscillatory ◽  
Essentially Nonoscillatory

Population balance equations (PBEs) are the main governing equations to model the processes of crystallization. Two-dimensional PBEs refer to the crystals that grow anisotropically with the change of two internal coordinates. Since the PBEs are hyperbolic equations, it is necessary to build up high resolution schemes to avoid numerical diffusion and numerical dispersion in order to obtain the accurate crystal size distribution (CSD). In this work, a 5th order weighted essentially nonoscillatory (WENO) method is introduced to compute the two-dimensional PBEs. Several numerical benchmark examples from literatures are carried out; it is found that WENO method has higher resolution than HR method which is well established. Therefore, WENO method is recommended in crystallization simulation when the crystal size distributions are sharp and higher accuracy is needed.

scholarly journals On blowing-up solutions for multi-time nonlinear hyperbolic equations and systems

Filomat ◽  
2017 ◽  
Vol 31 (9) ◽  
pp. 2599-2609
Author(s):  
B. Ahmad ◽  
A. Alsaedi ◽  
E. Cuesta ◽  
M. Kirane
Keyword(s):  
Nonlinear Equation ◽  
Hyperbolic Equation ◽  
Space Dimension ◽  
Hyperbolic Equations ◽  
Nonlinear Hyperbolic Equation ◽  
Two Dimensional ◽  
Nonlinear Hyperbolic Equations ◽  
Blowing Up ◽  
Time Order ◽  
Blowing Up Solutions

For a two-dimensional time nonlinear hyperbolic equation with a power nonlinearity, a threshold exponent depending on the space dimension is presented. Furthermore, the analysis is extended not only to a system of two equations but also to a two-time fractional nonlinear equation with different time order derivatives.

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