A novel algorithm for the computation of systems containing different types of integral and integro‐differential equations

Khan, Noor Saeed; Ali, Liaqat; Ali, Rohail; Thounthong, Phatiphat

doi:10.1002/htj.22018

Cited by 12 publications

(8 citation statements)

References 49 publications

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“…The suggested method comprises solely of a series in which the undefined constants are found in the conventional manner. The results achieved using the method are in good agreement with the exact solution, demonstrating that it both effective and simple to use [4]. The Lyapunov's functional technique is used to conduct new research on the stability, asymptotically stability and instability of the zero solution, boundedness, integrability of solutions and integrability of derivatives of solutions of certain nonlinear (DIDEs).…”

Section: Introductionmentioning

confidence: 66%

Hermite Polynomial and Least-Squares Technique for Solving Integro-differential Equations

Shoushan

2022

EJMS

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The goal of this project is to offer a new technique for solving integro-differential equations (IDEs) with mixed circumstances, which is based on the Hermite polynomial and the Least-Squares Technique (LST). Three examples will be given to demonstrate how the suggested technique works. The numerical results were utilized to demonstrate the correctness and efficiency of the existing method, and all calculations were carried out with the help of the MATLAB R2018b program.

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Section: Introductionmentioning

confidence: 66%

Hermite Polynomial and Least-Squares Technique for Solving Integro-differential Equations

Shoushan

2022

EJMS

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“…4 are predefined sufficiently small constants for the 1-st iteration. By solving the SOS-based stability condition in (20) to (25), we can obtain the solution for the 2-nd iteration: X (2) (x(t)) and N (2) (x(t)). Also, G (2) (x(t)) = N (2) (x(t))X (2) (x(t)) −1 .…”

Section: Iterative Stability Analysismentioning

confidence: 99%

“…The research works focus on the domains of attraction for polynomial nonlinear systems were reported in [8,9] Also the approaches in [10][11][12][13][14][15][16][17][18] adopted polynomial terms in the fuzzy-model-based (FMB) control. It is worth mentioning that the SOSbased techniques also have the potential to be applied to solve the dynamic problems in the heat transfer investigation [19][20][21].…”

Section: Introductionmentioning

confidence: 99%

Iterative stability analysis for general polynomial control systems

2021

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The main challenge of the stability analysis for general polynomial control systems is that non-convex terms exist in the stability conditions, which hinders solving the stability conditions numerically. Most approaches in the literature impose constraints on the Lyapunov function candidates or the non-convex related terms to circumvent this problem. Motivated by this difficulty, in this paper, we confront the non-convex problem directly and present an iterative stability analysis to address the long-standing problem in general polynomial control systems. Different from the existing methods, no constraints are imposed on the polynomial Lyapunov function candidates. Therefore, the limitations on the Lyapunov function candidate and non-convex terms are eliminated from the proposed analysis, which makes the proposed method more general than the state-of-the-art. In the proposed approach, the stability for the general polynomial model is analyzed and the original non-convex stability conditions are developed. To solve the non-convex stability conditions through the sum-of-squares programming, the iterative stability analysis is presented. The feasible solutions are verified by the original non-convex stability conditions to guarantee the asymptotic stability of the general polynomial system. The detailed simulation example is provided to verify the effectiveness of the proposed approach. The simulation results show that the proposed approach is more capable to find feasible solutions for the general polynomial control systems when compared with the existing ones.

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“…The present article investigates bioconvection Casson nanoliquid film sprayed on a stretching cylinder in the presence of homogeneous-heterogeneous chemical reactions using HAM solution [60][61][62][63][64][65].…”

Section: Introductionmentioning

confidence: 99%

Bioconvection Casson nanoliquid film sprayed on a stretching cylinder in the portfolio of homogeneous‐heterogeneous chemical reactions

et al. 2022

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In chemical engineering, the materials that is drawn or stretched continuously its surface velocity initially increases with distance from the orifice. The extruded material is also simultaneously cooled to provide solidification through a water bath or spraying with a coolant. Due to such applications and others, the present study concerns with the film deposition of Casson nanoliquid heat and mass transfer bioconvection flow with homogeneous‐heterogeneous chemical reactions, entropy generation, thermal radiation and magnetic dipole effects. The mechanical system has been proposed by the governing equations and boundary conditions which are simplified by the use of suitable similarity transformations. Homotopy analysis method is applied to obtain the series solution of non‐linear ordinary differential equations. Physical behaviors of heat and mass transfer flow with entropy generation and spray rate are investigated through the embedded parameters. Velocity is decreased with Casson nanofluid, ferromagnetic, porosity and inertial parameters while temperature is increased with thermal radiation, ferromagnetic, porosity and inertial parameters. Concentration of chemical reaction is increased with Schmidt and Reynolds numbers as well as heterogeneous chemical reaction parameter while motile microorganisms concentration is decreased with bioconvection Lewis, Peclet, and Reynolds numbers. Entropy generation is increased with thermal radiation, diffusivity and porosity parameters while spray rate is decreased with high values of film size.

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A novel algorithm for the computation of systems containing different types of integral and integro‐differential equations

Cited by 12 publications

References 49 publications

Hermite Polynomial and Least-Squares Technique for Solving Integro-differential Equations

Hermite Polynomial and Least-Squares Technique for Solving Integro-differential Equations

Iterative stability analysis for general polynomial control systems

Bioconvection Casson nanoliquid film sprayed on a stretching cylinder in the portfolio of homogeneous‐heterogeneous chemical reactions

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