Application of the hybrid method with constant coefficients to solving the integro-differential equations of first order

2012 ◽  
Author(s):  
Galina Mehdiyeva ◽  
Mehriban Imanova ◽  
Vagif Ibrahimov
Keyword(s):  
Differential Equations ◽  
Hybrid Method ◽  
First Order ◽  
Constant Coefficients

First-order systems of linear partial differential equations: normal forms, canonical systems, transform methods

2014 ◽  
Vol 13 (1) ◽  
pp. 109-132
Author(s):  
Heinz Toparkus
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Alternative View ◽  
Partial Differential ◽  
Transform Methods ◽  
Canonical Systems ◽  
First Order ◽  
Linear Partial Differential Equations ◽  
Elementary Methods ◽  
Constant Coefficients

Abstract In this paper we consider first-order systems with constant coefficients for two real-valued functions of two real variables. This is both a problem in itself, as well as an alternative view of the classical linear partial differential equations of second order with constant coefficients. The classification of the systems is done using elementary methods of linear algebra. Each type presents its special canonical form in the associated characteristic coordinate system. Then you can formulate initial value problems in appropriate basic areas, and you can try to achieve a solution of these problems by means of transform methods.

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.

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