An embedded method for integrating systems of structurally separated ordinary differential equations

Eremin, Alexey; Olemskoy, Igor V.

doi:10.1134/s0965542510030048

Cited by 5 publications

(3 citation statements)

References 5 publications

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“…Figure 5 presents absolute displacement in the plane XY. The comparison of the results was performed with the numerical results that are obtained by solving the Cauchy problem for systems of differential equations using numerical method of Dormand-Prince [17], which considers structural features of the equations [18], and can be successfully used for solving differential equations in partial derivatives [19][20][21]. The difference between the maximum deviations is less than 2%.…”

Section: Mathematical Model Of the System Of Drilling Rigmentioning

confidence: 99%

Mathematical modeling of the system of drilling rig

Kolpak¹,

Ivanov²

2015

ces

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A nonlinear mathematical model of the system of drilling rig, consisting of the rig, the control cabin, the working platform and platforms with engines has been developed. The mathematical model of the rig with six degrees of freedom is represented by a system of nonlinear ordinary differential equations. The methodology for calculation the basic characteristics of oscillation using the method of polynomial transformations was developed. The formulas for the calculation by the method of polynomial transformations were obtained.

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Section: Mathematical Model Of the System Of Drilling Rigmentioning

confidence: 99%

Mathematical modeling of the system of drilling rig

Kolpak¹,

Ivanov²

2015

ces

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“…The methods proposed there need fewer righthand side evaluations than the classic methods which do not use structural properties. The examples of such methods were derived and compared to the wide-known computational schemes in [8,10] and in a number of papers by the authors, issued only in Russian.…”

Section: Introductionmentioning

confidence: 99%

“…However, for y i and y j the number of stages can be reduced. Thus in [10] a method of order five with effective (using First Same as Last technique) six stages for y 0 and five stages for each y i and y j was constructed, while the classic method takes six stages for any unknown. For lower order methods same effect was also obtained [9].…”

Section: Introductionmentioning

confidence: 99%

Embedded methods of order six for special systems of ordinary differential equations

Olemskoy¹,

Eremin²,

Kovrizhnykh³

2017

ams

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An embedded pair of Runge-Kutta methods of orders six and four for structurally partitioned systems of ordinary differential equations is constructed. The Dormand-Prince approach to automatic step-size control is used. The coefficients of the constructed methods are presented. The method has seven stages, however the First-Same-as-Last technique further reduces the computational cost. Thus the presented scheme is more effective than existing classical methods of order six.Mathematics Subject Classification: 65L05, 65L06

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