In this paper, a class of A()-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 and stiffly stable for and . Some numerical results are reported to illustrate the method.
For initial value problem (IVPs) in ordinary second order differential equations of the special form 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...
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-stable for step length .
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