Convergent Finite Difference Schemes for Nonlinear Parabolic Equations

1972 ◽  
Vol 9 (4) ◽  
pp. 523-533 ◽  
Author(s):  
Albert C. Reynolds, Jr.
Keyword(s):  
Finite Difference ◽  
Parabolic Equations ◽  
Nonlinear Parabolic Equations ◽  
Difference Schemes ◽  
Finite Difference Schemes ◽  
Nonlinear Parabolic

Stability of Finite-difference Schemes for Semilinear Multidimensional Parabolic Equations

2012 ◽  
Vol 12 (3) ◽  
pp. 289-305 ◽  
Author(s):  
Bosko Jovanovic ◽  
Magdalena Lapinska-Chrzczonowicz ◽  
Aleh Matus ◽  
Piotr Matus
Keyword(s):  
Finite Difference ◽  
Parabolic Equations ◽  
Blow Up ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Difference Schemes ◽  
Finite Difference Schemes ◽  
Nonlinear Odes ◽  
The Stability ◽  
Initial Boundary Value

Abstract Abstract — We have studied the stability of finite-difference schemes approximating initial-boundary value problem (IBVP) for multidimensional parabolic equations with a nonlinear source of a power type. We have obtained simple sufficient input data conditions, in which the solutions of differential and difference problems are globally bounded for all t. It is shown that if these conditions are not satisfied, then the solution can blow-up (go to infinity) in finite time. The lower bound of the blow-up time has been determined. The stability of the difference solution has been proven. In all cases, we used the method of energy inequalities based on the application of the Chaplygin comparison theorem for nonlinear ODEs, Bihari-type inequalities and their discrete analogs.

Conservative Finite Difference Schemes to a Nonlinear Parabolic System of Cancer Invasion

2011 ◽  
Author(s):  
Mikhail K. Kolev ◽  
Lubin G. Vulkov ◽  
George Venkov ◽  
Ralitza Kovacheva ◽  
Vesela Pasheva
Keyword(s):  
Finite Difference ◽  
Parabolic System ◽  
Cancer Invasion ◽  
Difference Schemes ◽  
Finite Difference Schemes ◽  
Nonlinear Parabolic System ◽  
Nonlinear Parabolic
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