Commutativity of Sixth-Order Time-Varying Linear Systems

Ibrahim, Salisu; Köksal, Mehmet Emir

doi:10.1007/s00034-021-01709-6

Cited by 10 publications

(4 citation statements)

References 14 publications

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“…The authors in (Ibrahim, & Koksal, 2021a) studied the commutativity with non-zero initial conditions (ICs) and their effects on the sensitivity was studied in [Salisu, I, 2022a;Salisu, I, 2022c] while the realization and decomposition of a fourth-order LTVSs with nonzero ICs by cascaded two Second-Order commutative pairs was introduced by (Ibrahim, & Koksal, 2021b;Salisu, & Rababah, 2022). The authors in (Rababah, & Ibrahim, 2016a;Rababah, & Ibrahim, 2016b;Rababah, & Ibrahim, 2018) come up with a numerical approximative process for degree reduction of curves and surface which approaches can be used to solve complex ODES, PDEs, and FDEs.…”

Section: Introductionmentioning

confidence: 99%

Application of Lagrange Interpolation Method to Solve First-Order Differential Equation Using Newton Interpolation Approach

2023

EAJSE

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One of the important problems in mathematics is finding the analytic solution and numerical solution of the differential equation using various methods and techniques. Most of the researchers tackled different numerical approaches to solve ordinary differential equations. These methods such as the Runge Kutta method, Euler's method, and Taylor's polynomial method have so many issues like difficulties in finding the solution that can lead to singularities or no solution. In this work, we considered Newton's interpolation and Lagrange's interpolation polynomial method (LIPM). These studies combine both Newton's interpolation method and Lagrange method (NIPM) to solve first-order differential equations. The results obtained provide minimum approximative error. The result is supported by solving an example.

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Section: Introductionmentioning

confidence: 99%

Application of Lagrange Interpolation Method to Solve First-Order Differential Equation Using Newton Interpolation Approach

2023

EAJSE

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“…The authors (Ibrahim, & Koksal, 2021a) studied the commutativity with non-zero initial conditions (ICs), and their effects on the sensitivity were studied (Salisu, 2022a;Salisu, 2022c) while the realization and decomposition of a fourth-order LTVSs with nonzero ICs by cascaded two Second-Order commutative pairs was introduced by (Ibrahim, & Koksal, 2021b;Salisu, & Rababah, 2022). The authors (Rababah, & Ibrahim, 2016a;Rababah, & Ibrahim, 2016b;Rababah, & Ibrahim, 2018) come up with a numerical approximative process for degree reduction of curves and surfaces which approaches can be used to solve complex ODES, PDEs, and FDEs.…”

Section: Introductionmentioning

confidence: 99%

Explicit Solution of First-Order Differential Equation Using Aitken’s and Newton’s Interpolation Methods

2023

EAJSE

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The struggle to find the analytic solution of several differential equations leads to several issues like difficulty in finding solutions, singularities, convergent issues, and stability. Because of these problems, most of the researchers come up with explicit approaches such as the Runge Kutta method, Euler's method, and Taylor's polynomial method for finding numerical solutions to the ordinary differential equation. In this work, we combine both the Aitken methods and Newton's interpolation method (NIM) to solve first-order differential equations. The numerical results obtained provide minimal error. The result is supported by solving an example.

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“…This means that commutativity is important from a practical point of view. (Ibrahim, & Koksal, 2021a)examined commutativity and its effect on sensitivity when there are non-zero starting conditions (ICs). Meanwhile, using cascaded pairs of secondorder commutative systems, (Salisu, 2022a;Salisu, 2022c) explored the realization and decomposition of fourth-order Linear Time-Varying Systems (LTVSs) with non-zero ICs.…”

Section: Introductionmentioning

confidence: 99%

Solution of First-Order Differential Equation Using Fourth-Order Runge-Kutta Approachand Adams Bashforth Methods

Salisu Ibrahim

2023

IJRITCC

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In this research, we investigate the solution of first-order differential equations(DEs) using Runge- Kutta fourth-order method (RKM) and Adams-Bashforth methods (ABMs). In this work we considerfourth-order RKM and ABMs for solving first order DEs. The method proof to be simple, easy, accurate and efficient technique for solving first order DEs. Moreover, there are unlimited application of fourth-order RK4 and ABMs for solving first-order DE in science, engineering, economics, social science, biology and business. These play an important role in science and engineering. Some examples are giving and solved to support the efficiency of our methods which are demonstrated by figures.

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Commutativity of Sixth-Order Time-Varying Linear Systems

Cited by 10 publications

References 14 publications

Application of Lagrange Interpolation Method to Solve First-Order Differential Equation Using Newton Interpolation Approach

Application of Lagrange Interpolation Method to Solve First-Order Differential Equation Using Newton Interpolation Approach

Explicit Solution of First-Order Differential Equation Using Aitken’s and Newton’s Interpolation Methods

Solution of First-Order Differential Equation Using Fourth-Order Runge-Kutta Approachand Adams Bashforth Methods

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