Abstract
This paper presents a study on the development and implementation of a second derivative method for the solution of stiff first order initial value problems of ordinary differential equations using method of interpolation and collocation of polynomial approximate solution. The results of this paper bring some useful information. The constructed methods are A-stable up to order 8. As it is shown in the numerical examples, the new methods are superior for stiff systems.
Highlights
We considered development of second derivative method for the solution of=y′ f ( x, y), y ( x= n ) y0, xn ≤ x ≤ xN (1)where xn is the initial points, y :[ xn, xN ] → Rm, f :[ xn, xN ]× R → Rm is continuous and at least twice differentiable
This paper presents a study on the development and implementation of a second derivative method for the solution of stiff first order initial value problems of ordinary differential equations using method of interpolation and collocation of polynomial approximate solution
The constructed methods are A-stable up to order 8. As it is shown in the numerical examples, the new methods are superior for stiff systems
Summary
Where xn is the initial points, y :[ xn , xN ] → Rm , f :[ xn , xN ]× R → Rm is continuous and at least twice differentiable. Several authors such as Enright [2], Enright and Pryce [3], Brown [4], Cash [5], Okunuga [6], Abhilimen and Okunuga [7], Ngwane and Jator [8], and Yakubu and Markus [9] have developed second derivative methods for the solution of (1) whose solution has exponential functions. The three methods recovered are tested on some numerical examples and their results compared with each other in order to determine how to fix the varying step-lengths to obtain the best results as shown Tables 1-4
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