scholarly journals On the derivation of second order variable step variable order block backward differentiation formulae for solving stiff ODEs

2013 ◽  
Author(s):  
Siti Ainor Mohd Yatim ◽  
Zarina Bibi Ibrahim ◽  
Khairil Iskandar Othman ◽  
Mohamed Suleiman
Keyword(s):  
Second Order ◽  
Variable Order ◽  
Stiff Odes ◽  
Variable Step ◽  
Order Variable ◽  
Backward Differentiation Formulae

A variable-step variable-order algorithm for systems of stiff odes

1997 ◽  
Vol 63 (1-2) ◽  
pp. 149-157 ◽  
Author(s):  
T. Van Hecke ◽  
G. Vanden G Berghe ◽  
M. Van Daele ◽  
H De Meyer
Keyword(s):  
Variable Order ◽  
Stiff Odes ◽  
Variable Step ◽  
Order Algorithm

Variable-step-size second-order-derivative multistep method for solving first-order ordinary differential equations in system simulation

2020 ◽  
Vol 11 (01) ◽  
pp. 2050001
Author(s):  
Lei Zhang ◽  
Chaofeng Zhang ◽  
Mengya Liu
Keyword(s):  
Differential Equations ◽  
Numerical Method ◽  
Multistep Method ◽  
Second Order ◽  
Order Derivative ◽  
Variable Step Size ◽  
Variable Order ◽  
Step Size ◽  
Variable Step ◽  
The Stability

According to the relationship between truncation error and step size of two implicit second-order-derivative multistep formulas based on Hermite interpolation polynomial, a variable-order and variable-step-size numerical method for solving differential equations is designed. The stability properties of the formulas are discussed and the stability regions are analyzed. The deduced methods are applied to a simulation problem. The results show that the numerical method can satisfy calculation accuracy, reduce the number of calculation steps and accelerate calculation speed.

scholarly journals Solving Directly Higher Order Ordinary Differential Equations by Using Variable Order Block Backward Differentiation Formulae

Symmetry ◽  
2019 ◽  
Vol 11 (10) ◽  
pp. 1289
Author(s):  
Asnor ◽  
Mohd Yatim ◽  
Ibrahim
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Higher Order ◽  
Computational Effort ◽  
Variable Order ◽  
Numerical Efficiency ◽  
Stiff Odes ◽  
Backward Differentiation Formulae ◽  
Bdf Method ◽  
Selection Of

Variable order block backward differentiation formulae (VOHOBBDF) method is employedfor treating numerically higher order Ordinary Differential Equations (ODEs). In this respect, the purpose of this research is to treat initial value problem (IVP) of higher order stiff ODEs directly. BBDF method is symmetrical to BDF method but it has the advantage of producing more than one solutions simultaneously. Order three, four, and five of VOHOBBDF are developed and implemented as a single code by applying adaptive order approach to enhance the computational efficiency. This approach enables the selection of the least computed LTE among the three orders of VOHOBBDF and switch the code to the method that produces the least LTE for the next step. A few numerical experiments on the focused problem were performed to investigate the numerical efficiency of implementing VOHOBBDF methods in a single code. The analysis of the experimental results reveals the numerical efficiency of this approach as it yielded better performances with less computational effort when compared with built-in stiff Matlab codes. The superior performances demonstrated by the application of adaptive orders selection in a single code thus indicate its reliability as a direct solver for higher order stiff ODEs.

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