Accelerating multi-dimensional combustion simulations using GPU and hybrid explicit/implicit ODE integration

2012 ◽  
Vol 159 (7) ◽  
pp. 2388-2397 ◽  
Author(s):  
Yu Shi ◽  
William H. Green ◽  
Hsi-Wu Wong ◽  
Oluwayemisi O. Oluwole
Keyword(s):  
Implicit Ode

scholarly journals Mathematical analysis of nonlocal PDEs for network generation

2019 ◽  
Vol 14 (5) ◽  
pp. 506
Author(s):  
Tobias Böhle ◽  
Christian Kuehn
Keyword(s):  
Partial Differential Equations ◽  
Numerical Simulations ◽  
Mathematical Analysis ◽  
Degree Distribution ◽  
Network Science ◽  
Steady States ◽  
Network Generation ◽  
First Order ◽  
First Order Pde ◽  
Implicit Ode

In this paper, we study a certain class of nonlocal partial differential equations (PDEs). The equations arise from a key problem in network science, i.e., network generation from local interaction rules, which result in a change of the degree distribution as time progresses. The evolution of the generating function of this degree distribution can be described by a nonlocal PDE. To address this equation we will rigorously convert it into a local first order PDE. Then, we use theory of characteristics to prove solvability and regularity of the solution. Next, we investigate the existence of steady states of the PDE. We show that this problem reduces to an implicit ODE, which we subsequently analyze. Finally, we perform numerical simulations, which show stability of the steady states.

scholarly journals On theoretical upper limits for valid timesteps of implicit ODE methods

2019 ◽  
Vol 4 (6) ◽  
pp. 1841-1853
Author(s):  
Kevin R. Green ◽  
◽  
George W. Patrick ◽  
Raymond J. Spiteri ◽  
Keyword(s):  
Upper Limits ◽  
Implicit Ode

Switching between modified Newton and fix-point iteration for implicit ode-solvers

1986 ◽  
Vol 26 (3) ◽  
pp. 339-348 ◽  
Author(s):  
Syvert P. Nørsett ◽  
Per G. Thomsen
Keyword(s):  
Fix Point ◽  
Implicit Ode

scholarly journals Extending explicit and linearly implicit ODE solvers for index-1 DAEs

2015 ◽  
Vol 82 ◽  
pp. 283-292 ◽  
Author(s):  
Matthew T. Lawder ◽  
Venkatasailanathan Ramadesigan ◽  
Bharatkumar Suthar ◽  
Venkat R. Subramanian
Keyword(s):  
Implicit Ode
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