Numerical Solutions to Poisson Equations Using the Finite-Difference Method [Education Column]

2014 ◽  
Vol 56 (4) ◽  
pp. 209-224 ◽  
Author(s):  
James R. Nagel
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Numerical Solutions ◽  
Poisson Equations ◽  
The Finite Difference Method

A Remark on the Courant-Friedrichs-Lewy Condition in Finite Difference Approach to PDE’s

2014 ◽  
Vol 6 (5) ◽  
pp. 693-698 ◽  
Author(s):  
Kosuke Abe ◽  
Nobuyuki Higashimori ◽  
Masayoshi Kubo ◽  
Hiroshi Fujiwara ◽  
Yuusuke Iso
Keyword(s):  
Mathematical Model ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Numerical Experiments ◽  
Numerical Solutions ◽  
Hyperbolic Partial Differential Equations ◽  
View Point ◽  
Rounding Errors ◽  
The Finite Difference Method

AbstractThe Courant-Friedrichs-Lewy condition (The CFL condition) is appeared in the analysis of the finite difference method applied to linear hyperbolic partial differential equations. We give a remark on the CFL condition from a view point of stability, and we give some numerical experiments which show instability of numerical solutions even under the CFL condition. We give a mathematical model for rounding errors in order to explain the instability.

scholarly journals Numerical Solutions with Linearization Techniques of the Fractional Harry Dym Equation

2019 ◽  
Vol 4 (1) ◽  
pp. 35-42 ◽  
Author(s):  
Asıf Yokuş ◽  
Sema Gülbahar
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Numerical Solutions ◽  
Von Neumann ◽  
Non Linear ◽  
The Finite Difference Method ◽  
Dym Equation ◽  
Harry Dym Equation ◽  
Linearization Techniques

AbstractIn this study, numerical solutions of the fractional Harry Dym equation are investigated. Linearization techniques are utilized for non-linear terms existing in the fractional Harry Dym equation. The error norms L2 and L∞ are computed. Stability of the finite difference method is studied with the aid of Von Neumann stabity analysis.

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