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A ( $α$ )-Stable Linear Multistep Methods for Stiff IVPs in ODEs

R. I. Okuonghae; M. N. O. Ikhile — 2011

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

In this paper, a class of A( $α$ )-stable linear multistep formulas for stiff initial value problems (IVPs) in ordinary differential equations (ODEs) is developed. The boundary locus of the methods shows that the schemes are A-stable for step number $k \leq 3$ and stiffly stable for $k = 4, 5$ and $6$ . Some numerical results are reported to illustrate the method.

Zero Dissipative DIRKN Pairs of Order 5(4) for Solving Special Second Order IVPs

S. O. Imoni; M. N. O. Ikhile — 2014

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

For initial value problem (IVPs) in ordinary second order differential equations of the special form $y^{''} = f (x, y)$ possessing oscillating solutions, diagonally implicit Runge–Kutta–Nystrom (DIRKN) formula-pairs of orders 5(4) in 5-stages are derived in this paper. The method is zero dissipative, thus it possesses a non-empty interval of periodicity. Some numerical results are presented to show the applicability of the new method compared with existing Runge–Kutta (RK) method applied to the problem reduced to...

The Numerical Solution of Stiff IVPs in ODEs Using Modified Second Derivative BDF

R. I. Okuonghae; M. N. O. Ikhile — 2012

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

This paper considers modified second derivative BDF (MSD-BDF) for the numerical solution of stiff initial value problems (IVPs) in ordinary differential equations (ODEs). The methods are A $(α)$ -stable for step length $k \leq 7$ .

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Currently displaying 1 – 3 of 3

A ( α )-Stable Linear Multistep Methods for Stiff IVPs in ODEs

Zero Dissipative DIRKN Pairs of Order 5(4) for Solving Special Second Order IVPs

The Numerical Solution of Stiff IVPs in ODEs Using Modified Second Derivative BDF

A ( $α$ )-Stable Linear Multistep Methods for Stiff IVPs in ODEs