scholarly journals Parallel Direct Integration Variable Step Block Method for Solving Large System of Higher Order Ordinary Differential Equations

10.5772/8201 ◽  
2009 ◽  
Author(s):  
Zanariah Abdul ◽  
Mohamed Suleim
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Higher Order ◽  
Large System ◽  
Direct Integration ◽  
Block Method ◽  
Integration Variable ◽  
Variable Step

scholarly journals Solving Nonstiff Higher-Order Ordinary Differential Equations Using 2-Point Block Method Directly

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
Hazizah Mohd Ijam ◽  
Mohamed Suleiman ◽  
Ahmad Fadly Nurullah Rasedee ◽  
Norazak Senu ◽  
Ali Ahmadian ◽  
...  
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Difference Method ◽  
Divided Difference ◽  
Approximate Solutions ◽  
Higher Order ◽  
Numerical Results ◽  
The Other ◽  
Block Method ◽  
Better Than

We describe the development of a 2-point block backward difference method (2PBBD) for solving system of nonstiff higher-order ordinary differential equations (ODEs) directly. The method computes the approximate solutions at two points simultaneously within an equidistant block. The integration coefficients that are used in the method are obtained only once at the start of the integration. Numerical results are presented to compare the performances of the method developed with 1-point backward difference method (1PBD) and 2-point block divided difference method (2PBDD). The result indicated that, for finer step sizes, this method performs better than the other two methods, that is, 1PBD and 2PBDD.

scholarly journals An Order Six Stormer-cowell-type Method for Solving Directly Higher Order Ordinary Differential Equations

2018 ◽  
Vol 11 (3) ◽  
pp. 1-12
Author(s):  
S. J. Kayode ◽  
O. S. Ige ◽  
F. O. Obarhua ◽  
E. O. Omole
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Higher Order ◽  
Type Method

Pathwise convergent higher order numerical schemes for random ordinary differential equations

2007 ◽  
Vol 463 (2087) ◽  
pp. 2929-2944 ◽  
Author(s):  
Peter E Kloeden ◽  
Arnulf Jentzen
Keyword(s):  
Stochastic Process ◽  
Brownian Motion ◽  
Vector Field ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Higher Order ◽  
Time Variable ◽  
Numerical Schemes ◽  
Hölder Continuous ◽  
Usual Order

Random ordinary differential equations (RODEs) are ordinary differential equations (ODEs) with a stochastic process in their vector field. They can be analysed pathwise using deterministic calculus, but since the driving stochastic process is usually only Hölder continuous in time, the vector field is not differentiable in the time variable, so traditional numerical schemes for ODEs do not achieve their usual order of convergence when applied to RODEs. Nevertheless deterministic calculus can still be used to derive higher order numerical schemes for RODEs via integral versions of implicit Taylor-like expansions. The theory is developed systematically here and applied to illustrative examples involving Brownian motion and fractional Brownian motion as the driving processes.

Parallel R-Point Explicit Block Method for Solving Second Order Ordinary Differential Equations Directly

2002 ◽  
Vol 79 (3) ◽  
pp. 551-560 ◽  
Author(s):  
Z. Omar ◽  
M. Sulaiman ◽  
M. Y. Saman ◽  
D. J. Evans
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Second Order ◽  
Block Method
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