P-stable singlestep methods for periodic initial-value problems involving second-order differential equations
Tóm tắt
A class of P-stable singlestep methods is discussed for solving initial-value problems involving second-order differential equations. The methods depend upon a parameter p>0 and reduce to the classical methods for p=0. A few choices of p have been discussed for which the methods are P-stable. Further, when p is chosen for linear problems as the square of the frequency of the periodic solution, the methods are P-stable. Numerical results for both linear and non-linear problems show that the P-stability is an important requirement for determining periodic numerical solutions of second-order differential equations.
Tài liệu tham khảo
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