Classification of Difference Schemes of Maximum Possible Accuracy on Extended Symmetric Stencils for the Schrödinger Equation and the Heat Conduction Equation

2020 ◽  
Vol 13 (1) ◽  
pp. 82-94
Author(s):  
V. I. Paasonen
Keyword(s):  
Heat Conduction ◽  
Schrödinger Equation ◽  
Heat Conduction Equation ◽  
Schrodinger Equation ◽  
Difference Schemes ◽  
Conduction Equation

Difference Schemes with Nonlocal Boundary Conditions

2001 ◽  
Vol 1 (1) ◽  
pp. 62-71 ◽  
Author(s):  
Alexei V. Goolin ◽  
Nikolai I. Ionkin ◽  
Valentina A. Morozova
Keyword(s):  
Heat Conduction ◽  
Boundary Conditions ◽  
Heat Conduction Equation ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Conditions ◽  
Difference Schemes ◽  
Conduction Equation ◽  
The Stability ◽  
The One ◽  
Necessary And Sufficient

AbstractThe paper deals with the stability, with respect to initial data, of difference schemes that approximate the heat-conduction equation with constant coefficients and nonlocal boundary conditions. Some difference schemes are considered for the one-dimensional heat-conduction equation, the energy norm is constructed, and the necessary and sufficient stability conditions in this norm are established for explicit and weighted difference schemes.

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