A Quasi-Steady-State Solver for the Stiff Ordinary Differential Equations of Reaction Kinetics

2000 ◽  
Vol 164 (2) ◽  
pp. 407-428 ◽  
Author(s):  
David R. Mott ◽  
Elaine S. Oran ◽  
Bram van Leer
Keyword(s):  
Steady State ◽  
Differential Equations ◽  
Reaction Kinetics ◽  
Ordinary Differential Equations ◽  
Quasi Steady State ◽  
Stiff Ordinary Differential Equations

Kinetics of Biocatalytical Synergistic Reactions

2005 ◽  
Vol 10 (3) ◽  
pp. 223-233 ◽  
Author(s):  
J. Kulys
Keyword(s):  
Steady State ◽  
Analytical Solution ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Stationary State ◽  
Initial Rate ◽  
Kinetic Constants ◽  
Quasi Steady State ◽  
The Novel ◽  
Kinetics Of

Kinetics of biocatalytical synergistic reactions has been analyzed at non-stationary state (NSS) and at quasi steady state (QSS) conditions. The application to the model kinetic constants taken from the first type of the experiments shows that QSS can be established for the enzyme and the mediator at time less than 1 s. Therefore, the analytical solution of the initial rate (IR) may be produced at relevant to an experiment time, and the dependence of the IR on substrates concentration may be analyzed rather easy. The use of kinetic constants from the second type of reactions shows that QSS is formed for the enzyme but not for the mediator. For this reason the modeling of the synergistic process was performed by solving the ordinary differential equations (ODE). For this purpose the novel program KinFitSim (c) was used.

scholarly journals A NEW SUPERCLASS OF BLOCK BACKWARD DIFFERENTIATION FORMULA FOR STIFF ORDINARY DIFFERENTIAL EQUATIONS

2014 ◽  
Vol 07 (01) ◽  
pp. 1350034 ◽  
Author(s):  
M. B. Suleiman ◽  
H. Musa ◽  
F. Ismail ◽  
N. Senu ◽  
Z. B. Ibrahim
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Numerical Results ◽  
New Method ◽  
Differentiation Formula ◽  
Stiff Ordinary Differential Equations ◽  
Backward Differentiation Formula ◽  
Error Constant

A superclass of block backward differentiation formula (BBDF) suitable for solving stiff ordinary differential equations is developed. The method is of order 3, with smaller error constant than the conventional BBDF. It is A-stable and generates two points at each step of the integration. A comparison is made between the new method, the 2-point block backward differentiation formula (2BBDF) and 1-point backward differentiation formula (1BDF). The numerical results show that the method developed outperformed the 2BBDF and 1BDF methods in terms of accuracy. It also reduces the integration steps when compared with the 1BDF method.

scholarly journals Diagonally Implicit Block Backward Differentiation Formula with Optimal Stability Properties for Stiff Ordinary Differential Equations

Symmetry ◽  
2019 ◽  
Vol 11 (11) ◽  
pp. 1342 ◽  
Author(s):  
Hazizah Mohd Ijam ◽  
Zarina Bibi Ibrahim
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Triangular Matrix ◽  
Differentiation Formula ◽  
Stability Properties ◽  
Stiff Ordinary Differential Equations ◽  
Backward Differentiation Formula ◽  
Optimal Stability ◽  
Best Value ◽  
Selection Of

This paper aims to select the best value of the parameter ρ from a general set of linear multistep formulae which have the potential for efficient implementation. The ρ -Diagonally Implicit Block Backward Differentiation Formula ( ρ -DIBBDF) was proposed to approximate the solution for stiff Ordinary Differential Equations (ODEs) to achieve the research objective. The selection of ρ for optimal stability properties in terms of zero stability, absolute stability, error constant and convergence are discussed. In the diagonally implicit formula that uses a lower triangular matrix with identical diagonal entries, allowing a maximum of one lower-upper (LU) decomposition per integration stage to be performed will result in substantial computing benefits to the user. The numerical results and plots of accuracy indicate that the ρ -DIBBDF method performs better than the existing fully and diagonally Block Backward Differentiation Formula (BBDF) methods.

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