Difference schemes for nonlinear equations of Schr�dinger and parabolic type

1991 ◽  
Vol 30 (2) ◽  
pp. 106-116 ◽  
Author(s):  
F. F. Ivanauskas
Keyword(s):  
Nonlinear Equations ◽  
Parabolic Type ◽  
Difference Schemes

INVARIANT DIFFERENCE SCHEMES FOR PARABOLIC EQUATIONS WITH TRANSFORMATIONS OF INDEPENDENT VARIABLES

1999 ◽  
Vol 09 (01) ◽  
pp. 93-110 ◽  
Author(s):  
A. A. SAMARSKII ◽  
V. I. MAZHUKIN ◽  
P. P. MATUS ◽  
V. G. RYCHAGOV ◽  
I. SMUROV
Keyword(s):  
Parabolic Equations ◽  
A Priori Estimates ◽  
Order Approximation ◽  
A Priori ◽  
Parabolic Type ◽  
Difference Schemes ◽  
Invariance Property ◽  
Independent Variables ◽  
Priori Estimates ◽  
Nonstationary Equations

In this paper, invariant difference schemes for nonstationary equations under independent variables transformation constructed and investigated. Under invariance of difference scheme we mean its ability to preserve basic properties (stability, approximation, convergency, etc.) in various coordinate systems. Difference schemes of the second-order approximation that satisfy the invariance property are constructed for equations of parabolic type. Stability and convergency investigation of correspondent difference problems are carried out; a priori estimates in various grid norms are obtained.

On a class of Volterra nonlinear equations of parabolic type

2010 ◽  
Vol 216 (1) ◽  
pp. 236-240 ◽  
Author(s):  
Yuzhen Bai ◽  
Pingping Zhang
Keyword(s):  
Nonlinear Equations ◽  
Parabolic Type
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