Solution for nonlinear Riccati equation by block method

Rasedee, Ahmad Fadly Nurullah; Ijam, Hazizah Mohd; Sathar, Mohammad Hasan Abdul; Ishak, Norizarina; Hamzah, Suharman; Sahrim, Musab; Ismail, Ishak

doi:10.1063/1.5041602

Cited by 4 publications

(1 citation statement)

References 13 publications

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“…In previous research, authors successfully adapted the variable order step size backward difference formulation (VOSBF) for solving orbital problems with periodic solutions (see [35][36][37][38][39]). After the success of tackling ODEs with periodic solutions, we initiated this study to attempt approximating chaos attractors which proven to be a more challenging type of ODE.…”

Section: Numerical Results and Analysismentioning

confidence: 99%

Numerical analysis on chaos attractors using a backward difference formulation

Rasedee¹,

Sathar²,

Najib³

et al. 2022

Math. Model. Comput.

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The chaos attractor is a system of ordinary differential equations which is known for having chaotic solutions for certain parameter values and an initial condition. Research conducted in the current work establishes a backward difference algorithm to study these chaos attractors. Different types of chaos mapping, namely the Lorenz chaos, 'sandwich' chaos and 'horseshoe' chaos will be analyzed. Compared to other numerical methods, the proposed backward difference algorithm will show to be an efficient tool for analyzing solutions for the chaos attractors.

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Section: Numerical Results and Analysismentioning

confidence: 99%

Numerical analysis on chaos attractors using a backward difference formulation

Rasedee¹,

Sathar²,

Najib³

et al. 2022

Math. Model. Comput.

View full text Add to dashboard Cite

show abstract

Two-point block variable order step size multistep method for solving higher order ordinary differential equations directly

Rasedee

Sathar

Hamzah

et al. 2021

Journal of King Saud University - Science

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Solving Duffing Type Differential Equations using a Three-Point Block Variable Order Step Size Method

Rasedee

Sathar

Asbullah

et al. 2019

J. Phys.: Conf. Ser.

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This research proposes a three-point block method for solving Duffing type higher order ordinary differential equations (ODEs) which is also commonly referred as the Duffing oscillator. The research conducted implements a variable order step size technique for approximating the exact solution for the Duffing Oscillator. The proposed algorithm will be tested against various Duffing oscillators and numerical approximation will be compared with current viable methods. The accuracy and efficiency of the proposed method will be illustrated in the numerical results.

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Solution for nonlinear Riccati equation by block method

Cited by 4 publications

References 13 publications

Numerical analysis on chaos attractors using a backward difference formulation

Numerical analysis on chaos attractors using a backward difference formulation

Two-point block variable order step size multistep method for solving higher order ordinary differential equations directly

Solving Duffing Type Differential Equations using a Three-Point Block Variable Order Step Size Method

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