Mixed generalized iterative method for scalar first order non-linear initial value problem with applications

2018 ◽  
Author(s):  
M. Sowmya ◽  
Aghalaya S. Vatsala
Keyword(s):  
Iterative Method ◽  
Initial Value Problem ◽  
Initial Value ◽  
First Order ◽  
Non Linear

ORDER AND CONVERGENCE OF THE ENHANCED 3-POINT FULLY IMPLICIT SUPER CLASS OF BLOCK BACKWARD DIFFERENTIATION FORMULA FOR SOLVING INITIAL VALUE PROBLEM

2021 ◽  
Vol 5 (2) ◽  
pp. 442-446
Author(s):  
Muhammad Abdullahi ◽  
Hamisu Musa
Keyword(s):  
Initial Value Problem ◽  
Initial Value Problems ◽  
Sufficient Conditions ◽  
Initial Value ◽  
Differentiation Formula ◽  
Stiff Initial Value Problems ◽  
First Order ◽  
Backward Differentiation Formula ◽  
Fully Implicit ◽  
Necessary And Sufficient

This paper studied an enhanced 3-point fully implicit super class of block backward differentiation formula for solving stiff initial value problems developed by Abdullahi & Musa and go further to established the necessary and sufficient conditions for the convergence of the method. The method is zero stable, A-stable and it is of order 5. The method is found to be suitable for solving first order stiff initial value problems

scholarly journals Asymmetric bifurcation

1980 ◽  
Vol 21 (3) ◽  
pp. 297-304 ◽  
Author(s):  
S. Rosenblat
Keyword(s):  
Diffusion Equation ◽  
Initial Value Problem ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Initial Value ◽  
Linear Diffusion ◽  
Non Linear ◽  
Bifurcation And Stability

AbstractA study is made of a non-linear diffusion equation which admits bifurcating solutions in the case where the bifurcation is asymmetric. An analysis of the initial-value problem is made using the method of multiple scales, and the bifurcation and stability characteristics are determined. It is shown that a suitable interpretation of the results can lead to determination of the choice of the bifurcating solution adopted by the system.

scholarly journals A parameter uniform almost first order convergent numerical method for non-linear system of singularly perturbed differential equations

BIOMATH ◽  
2016 ◽  
Vol 5 (2) ◽  
pp. 1608111
Author(s):  
Ishwariya Raj ◽  
Princy Mercy Johnson ◽  
John J.H Miller ◽  
Valarmathi Sigamani
Keyword(s):  
Linear System ◽  
Differential Equations ◽  
Numerical Method ◽  
Shishkin Mesh ◽  
Singularly Perturbed ◽  
Initial Value ◽  
First Order ◽  
Non Linear ◽  
Perturbation Parameters ◽  
Non Linear System

In this paper an initial value problem for a non-linear system of two singularly perturbed first order differential equations is considered on the interval (0,1].The components of the solution of this system exhibit initial layers at 0. A numerical method composed of a classical finite difference scheme on a piecewise uniform Shishkin mesh is suggested. This method is proved to be almost first order convergent in the maximum norm uniformly in the perturbation parameters.

scholarly journals A Class of Explicit Integrators with o-grid Interpolation for Solving Non-linear Systems of First Order ODEs

2020 ◽  
pp. 106-118
Author(s):  
U. W. Sirisena ◽  
S. I. Luka ◽  
S. Y. Yakubu
Keyword(s):  
Research Work ◽  
Stability And Convergence ◽  
Initial Value ◽  
First Order ◽  
Non Linear ◽  
Improved Stability ◽  
Linear Problems ◽  
The Stability ◽  
Stability And Accuracy ◽  
Grid Interpolation

This research work is aimed at constructing a class of explicit integrators with improved stability and accuracy by incorporating an off-gird interpolation point for the purpose of making them effcient for solving stiff initial value problems. Accordingly, continuous formulations of a class of hybrid explicit integrators are derived using multi-step collocation method through matrix inversion technique, for step numbers k = 2; 3; 4: The discrete schemes were deduced from their respective continuous formulations. The stability and convergence analysis were carried out and shown to be A(α)-stable and convergent respectively. The discrete schemes when implemented as block integrators to solve some non-linear problems, it was observed that the results obtained compete favorably with the MATLAB ode23 solver.

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