An Numeric Method on the Third Order Term of KDV Equation

2011 ◽  
Vol 135-136 ◽  
pp. 253-255
Author(s):  
Yi Min Tian
Keyword(s):  
Difference Scheme ◽  
Kdv Equation ◽  
Order Term ◽  
Boundary Value ◽  
Difference Schemes ◽  
Boundary Values ◽  
Implicit Difference Scheme ◽  
Third Order ◽  
The Third ◽  
Numeric Experiment

Numeric scheme and numeric result was in this paper. First, We proposes a kind of explicit - implicit difference scheme to solve the initial and boundary value questions of the third order term of KDV equation here,and so we can solve the problem that the additional boundary values must be given first for present difference schemes when we try to realize the calculation by then., second, numeric experiment results was given ay the end of this article.

Method of calculating the aberrations of soft X-ray and vacuum ultraviolet optical systems

2019 ◽  
Vol 26 (5) ◽  
pp. 1558-1564
Author(s):  
Yiqing Cao ◽  
Zhijuan Shen ◽  
Zhixia Zheng
Keyword(s):  
Optical System ◽  
Vacuum Ultraviolet ◽  
Optical Systems ◽  
Third Order ◽  
Order Accuracy ◽  
X Ray ◽  
Plane Symmetric ◽  
The Third ◽  
Aberration Theory ◽  
Ray Coordinates

Based on the the third-order aberration theory of plane-symmetric optical systems, this paper studies the effect on aberrations of the second-order accuracy of aperture-ray coordinates and the extrinsic aberrations of this kind of optical system; their calculation expressions are derived. The resultant aberration expressions are then applied to calculate the aberrations of two design examples of soft X-ray and vacuum ultraviolet (XUV) optical systems; images are compared with ray-tracing results using SHADOW software to validate the aberration expressions. The study shows that the accuracy of the aberration expressions is satisfactory.

scholarly journals The accuracy of finite-difference schemes calculating the interaction of shock waves

2019 ◽  
Vol 485 (6) ◽  
pp. 691-696 ◽  
Author(s):  
V. V. Ostapenko ◽  
N. A. Khandeeva
Keyword(s):  
Finite Difference ◽  
Shock Waves ◽  
Difference Schemes ◽  
Weno Scheme ◽  
Shock Capturing ◽  
Finite Difference Schemes ◽  
Third Order ◽  
Interaction Of Shock Waves ◽  
Fifth Order

The accuracy with which the shock-capturing finite-difference schemes calculate the flows with interaction of shock waves is studied. It is shown that, in the domains between the shock waves after their incidence, the calculation accuracy of invariants of the combined schemes is several orders of magnitude higher than the accuracy of the WENO-scheme, which is fifth-order in space and third-order in time.

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