On the influence of integral perturbations to the asymptotic stability of solutions of a second-order linear differential equation

Iskandarov, S.; Abdiraiimova, Nazigai Abdinabievna

doi:10.1007/s10958-020-04969-w

Cited by 5 publications

(6 citation statements)

References 3 publications

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“…Differentiating the continuous formulation (9) with respect to µ and evaluating the derivative at µ = − 3h 2 results in (20). As explained earlier, the differentiation is important in this context because we want to obtain a square system of four equations in four unknowns.…”

Section: Derivation Of Multi-step Collocation Methodsmentioning

confidence: 99%

“…Similarly, Adee and Atabo [17] presented a two point linear multi-step method for solving similar problems as the ones considered in [7] and the present work, except that their method is non starting and they used a fourth order Runge-Kutta method in obtaining the starting values. In this work, our method is self-starting and does not rely on other methods to start (see also [18][19][20][21][22][23][24][25]. )…”

Section: Introductionmentioning

confidence: 99%

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Comparing the Performance of Two Butcher-Based Block Hybrid Algorithms for the Solution of Initial Value Problems

Akinola,

Shokri,

Sunday

et al. 2024

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In this paper, we compare the performances of two Butcher-based block hybrid methods for the numerical integration of initial value problems. We compare the condition numbers of the linear system of equations arising from both methods and the absolute errors of the solution obtained. The results of the numerical experiments illustrate that the better conditioned method outperformed its less conditioned counterpart based on the absolute errors. In addition, after applying our method on some examples, it was discovered that the absolute errors in this work were better than those of a recent study in the literature. Hence, we recommend this method for the numerical solution of stiff and non-stiff initial value problems.

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Section: Derivation Of Multi-step Collocation Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Comparing the Performance of Two Butcher-Based Block Hybrid Algorithms for the Solution of Initial Value Problems

Akinola,

Shokri,

Sunday

et al. 2024

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“…He 41 proposed a fractal model for internal temperature response in porous concrete, advancing understanding in applied mathematics. Iskandarov and Komartsova 42,57 investigated integral perturbations' influence on boundedness in fourth-order linear differential equations. Khankishiyev 43 employed finite differences to solve loaded differential equations, while 44 , 56 explored dark energy solutions without a cosmological constant.…”

Section: The Neutrosophic Statisticsmentioning

confidence: 99%

Estimating neutrosophic finite median employing robust measures of the auxiliary variable

Masood,

Ibrar,

Shabbir

et al. 2024

Sci Rep

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Our study explores neutrosophic statistics, an extension of classical and fuzzy statistics, to address the challenges of data uncertainty. By leveraging accurate measurements of an auxiliary variable, we can derive precise estimates for the unknown population median. The estimators introduced in this research are particularly useful for analysing unclear, vague data or within the neutrosophic realm. Unlike traditional methods that yield single-valued outcomes, our estimators produce ranges, suggesting where the population parameter is likely to be. We present the suggested generalised estimator's bias and mean square error within a first-order approximation framework. The practicality and efficiency of these proposed neutrosophic estimators are demonstrated through real-world data applications and the simulated data set.

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“…It is known that the qualitative approach does not seek explicit solutions but is concerned with the behaviour of solutions to differential equations. Since then, the asymptotic and oscillatory properties have attracted the attention of many researchers; see [4][5][6][7][8][9][10][11][12][13].…”

Section: Introductionmentioning

confidence: 99%

Second-Order Damped Differential Equations with Superlinear Neutral Term: New Criteria for Oscillation

Al-Jaser,

Cesarano,

Qaraad

et al. 2024

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This paper focuses on establishing new criteria to guarantee the oscillation of solutions for second-order differential equations with a superlinear and a damping term. New sufficient conditions are presented, aimed at analysing the oscillatory properties of the solutions to the equation under study. To prove these results, we employed various analysis methods, establishing new relationships to address certain problems that have hindered previous research. Consequently, by applying the principles of comparison and the Riccati transformation, we obtained findings that develop and complement those reported in earlier literature. The significance of our results is illustrated with several examples.

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On the influence of integral perturbations to the asymptotic stability of solutions of a second-order linear differential equation

Cited by 5 publications

References 3 publications

Comparing the Performance of Two Butcher-Based Block Hybrid Algorithms for the Solution of Initial Value Problems

Comparing the Performance of Two Butcher-Based Block Hybrid Algorithms for the Solution of Initial Value Problems

Estimating neutrosophic finite median employing robust measures of the auxiliary variable

Second-Order Damped Differential Equations with Superlinear Neutral Term: New Criteria for Oscillation

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