Controllability of process described by system of linear integro-differential equations with restrictions

Aisagaliev, S. A.; Sevryugin, I. V.

doi:10.1063/1.4959685

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2020

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“…The new method is from the second class. The purpose of this article is to introduce more efficient methods for the numerical solution of second‐order initial value problems with highly oscillatory solutions (see, eg, References 5‐36,37). To be more specific, the main aim of this article is to develop a new four‐step predictor P‐stable method which contains phase‐lag and some of the derivatives therein are equal to zero.…”

Section: Introductionmentioning

confidence: 99%

An efficient four‐step multiderivative method for the numerical solution of second‐order IVPs with oscillating solutions

Shokri

Khalsaraei

2020

Comp and Math Methods

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An explicit four‐step method of 10th algebraic order is constructed and analyzed in this article for the numerical integration of initial value problems of second‐order ordinary differential equations. The new method is multiderivative. It also has the most important P‐stability property for problems that have one frequency. The advantage of the new method is its simplicity in implementation and, since it is explicit, it will not require any additional predictor stages. Applying our new method to the well‐known problems such as Stiefel and Bettis “near periodic” problem, and Duffing's equation without damping, we found that the method has several advantages, such as simplicity, accuracy, stability, and efficiency.

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Section: Introductionmentioning

confidence: 99%