scholarly journals Time integration algorithm based on divergent series resummation, for ordinary and partial differential equations

2013 ◽  
Vol 236 ◽  
pp. 56-73 ◽  
Author(s):  
Dina Razafindralandy ◽  
Aziz Hamdouni
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Time Integration ◽  
Divergent Series ◽  
Partial Differential ◽  
Integration Algorithm ◽  
Time Integration Algorithm

scholarly journals Efficient Time Integration of Nonlinear Partial Differential Equations by Means of Rosenbrock Methods

Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 1970
Author(s):  
Isaías Alonso-Mallo ◽  
Begoña Cano
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Nonlinear Partial Differential Equations ◽  
Method Of Lines ◽  
Time Integration ◽  
Order Reduction ◽  
Linear Case ◽  
Boundary Values ◽  
Partial Differential ◽  
Rosenbrock Methods

We avoid as as much as possible the order reduction of Rosenbrock methods when they are applied to nonlinear partial differential equations by means of a similar technique to the one used previously by us for the linear case. For this we use a suitable choice of boundary values for the internal stages. The main difference from the linear case comes from the difficulty to calculate those boundary values exactly in terms of data. In any case, the implementation is cheap and simple since, at each stage, just some additional terms concerning those boundary values and not the whole grid must be added to what would be the standard method of lines.

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