scholarly journals An Accurate Implicit Quarter Step First Derivative Block Hybrid Method (AIQSFDBHM) for Solving Ordinary Differential Equations

2019 ◽  
pp. 1-13
Author(s):  
P. Tumba ◽  
J. Sabo ◽  
A. A. Okeke ◽  
D. I. Yakoko
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Hybrid Method ◽  
Numerical Experiments ◽  
Stability Region ◽  
Numerical Solutions ◽  
Initial Value ◽  
First Order ◽  
First Derivative ◽  
Stiff Odes

The new accurate implicit quarter step first derivative blocks hybrid method for solving ordinary differential equations have been proposed in this paper via interpolation and collocation method for the solution of stiff ODEs. The analysis of the method was study and it was found to be consistent, convergent, zero-stability, We further compute the region of absolute stability region and it was found to be Aα − stable . It is obvious that, the numerical experiments considered showed that the methods compete favorably with existing ones. Thus, the pair of numerical methods developed in this research is computationally reliable in solving first order initial value problems, as the results from numerical solutions of stiff ODEs shows that this method is superior and best to solve such problems as in tables and figures.

scholarly journals BBDF-Alpha for solving stiff ordinary differential equations with oscillating solutions

2020 ◽  
Vol 51 (2) ◽  
pp. 123-136
Author(s):  
Iskandar Shah Mohd Zawawi
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Numerical Experiments ◽  
Stability Region ◽  
Newton Iteration ◽  
Computational Time ◽  
First Order ◽  
Stiff Ordinary Differential Equations ◽  
Oscillating Solutions ◽  
The Stability

In this paper, the block backward differentiation α formulas (BBDF-α) is derived for solving first order stiff ordinary differential equations with oscillating solutions. The consistency and zero stability conditions are investigated to prove the convergence of the method. The stability region in the entire negative half plane shows that the derived method is A-stable for certain values of α. The implementation of the method using Newton iteration is also discussed. Several numerical experiments are conducted to demonstrate the performance of the method in terms of accuracy and computational time.

A Multiple Interval Chebyshev-Gauss-Lobatto Collocation Method for Ordinary Differential Equations

2016 ◽  
Vol 9 (4) ◽  
pp. 619-639 ◽  
Author(s):  
Zhong-Qing Wang ◽  
Jun Mu
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Collocation Method ◽  
Initial Value Problems ◽  
Numerical Experiments ◽  
High Order Accuracy ◽  
Nonlinear Ordinary Differential Equations ◽  
Initial Value ◽  
Order Accuracy ◽  
Long Time

AbstractWe introduce a multiple interval Chebyshev-Gauss-Lobatto spectral collocation method for the initial value problems of the nonlinear ordinary differential equations (ODES). This method is easy to implement and possesses the high order accuracy. In addition, it is very stable and suitable for long time calculations. We also obtain thehp-version bound on the numerical error of the multiple interval collocation method underH1-norm. Numerical experiments confirm the theoretical expectations.

On Axisymmetrical Deformations of Nonlinear Membranes

1970 ◽  
Vol 37 (4) ◽  
pp. 1002-1011 ◽  
Author(s):  
W. H. Yang ◽  
W. W. Feng
Keyword(s):  
Numerical Methods ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Elastic Stress ◽  
Material Behavior ◽  
System Of Equations ◽  
Initial Value ◽  
First Order ◽  
Stress Strain Relation ◽  
Flat Membrane

The mechanics problem concerning large axisymmetric deformations of nonlinear membranes is reformulated in terms of a system of three first-order ordinary differential equations with explicit derivatives. With a set of proper boundary conditions, arrangements are made to change the boundary-value problem into the form of an initial value problem such that the solution can be obtained by standard numerical methods for integrating ordinary differential equations. The system of equations derived applies to the class of all axisymmetric deformations of membranes with a general elastic stress-strain relation. Three examples are given on inflating of a flat membrane, longitudinal stretching of a tube, and flattening of a semispherical cap. In the examples, the Mooney model are assumed to describe the material behavior of the membranes. The solution on the flat membrane serves to compare with an existing one in literature. The solutions on the tube and the cap are new.

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