A note on variable step-size formulation of a Simpson’s-type second derivative block method for solving stiff systems

Ramos, Higinio; Singh, Gurjinder

doi:10.1016/j.aml.2016.08.012

Cited by 21 publications

(11 citation statements)

References 8 publications

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“…Based on the simulation results presented in subsection VI.2, the performance of this algorithm is acceptable in finding the extremum points of the signals After finding extremum points, R-parameter is calculated through Eq. 3 where, DC_IR and DC_RED represent the area below the minimum level of the IR and RED signals, respectively, while AC_IR is the area between DC_IR level and IR signal that is calculated through Simpson’s algorithm,[ 10 ] and AC_RED is the area between DC_RED level and RED signal, i.e. calculated through Simpson’s algorithm …”

Section: Proposed Smart Wristbandsmentioning

confidence: 99%

Wireless Patient Monitoring System Based on Smart Wristbands and Central user Interface Software

Vafaie,

Ahmadi Beni

2024

Journal of Medical Signals &Amp; Sensors

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In this article, a patient monitoring system is proposed that is able to obtain heart rate and oxygen saturation (SpO2) levels of patients, identify abnormal conditions, and inform emergency status to the nurses. The proposed monitoring system consists of smart patient wristbands, smart nurse wristbands, central monitoring user interface (UI) software, and a wireless communication network. In the proposed monitoring system, a unique smart wristband is dedicated to each of the patients and nurses. To measure heart rate and SpO2 level, a pulse oximeter sensor is used in the patient wristbands. The output of this sensor is transferred to the wristband’s microcontroller where heart rate and SpO2 are calculated through advanced signal processing algorithms. Then, the calculated values are transmitted to central UI software through a wireless network. In the UI software, received values are compared with their normal values and a predefined message is sent to the nurses’ wristband if an abnormal condition is identified. Whenever this message is received by a nurse’s wristband, an acoustic alarm with vibration is generated to inform an emergency status to the nurse. By doing so, health services are delivered to the patients more quickly and as a result, the probability of the patient recovery is increased effectively.

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Section: Proposed Smart Wristbandsmentioning

confidence: 99%

Wireless Patient Monitoring System Based on Smart Wristbands and Central user Interface Software

Vafaie,

Ahmadi Beni

2024

Journal of Medical Signals &Amp; Sensors

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“…If a fitted method is chosen then it may bring additional function evaluations and does not serve the purpose of a variable stepsize approach. There are several existing block-type methods as well as trigonometrically fitted methods that use an adaptive stepsize approach and use a non-fitted method for the embedding purpose (see, for example, [40,42]).…”

Section: Variable Stepsize Formulationmentioning

confidence: 99%

Optimizing A-stable hyperbolic fitting for time efficiency: exploring constant and variable stepsize approaches

Baleanu,

Qureshi,

Soomro

et al. 2024

J. Math. Computer Sci.

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This paper proposes an optimal time-efficient numerical method for solving the initial value problems (IVPs) of ordinary differential equations (ODEs) that is both A-stable and hyperbolically fitted. The method is designed to handle both constant and variable step sizes, making it highly adaptable to different types of ODEs. The methodology proposed herein leverages the optimization of an off-grid point, derived from the predominant term of the local truncation error, to enhance both accuracy and stability in the solution of stiff ODEs. This approach incorporates a variable step size control, predicated upon the error estimation furnished by the embedded pair, and aims to minimize computational expenses while concurrently safeguarding both precision and stability. Furthermore, the stability domain of the proposed method is demonstrated to be optimal, signifying it encompasses the maximal conceivable set of step sizes wherein the method retains its stability. Other important measures including zero-stability, consistency, and convergence are also discussed theoretically and confirmed experimentally. Numerical experiments consisting of the Duffing system, sinusoidal stiff system, periodic orbit system, two-body system, Lorenz system, and the system for catenary equation demonstrate that the proposed method is highly competitive in terms of accuracy and efficiency, and outperforms several existing methods for solving stiff ODEs with both constant and variable step sizes.

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“…e problem is also studied by Cash [28,29]. Problem was also solved with numerical integrators in [30,32,33]. It consists of a stiff system of three nonlinear ordinary differential equations…”

Section: Numerical Experimentsmentioning

confidence: 99%

A Family of $A$ -Stable Optimized Hybrid Block Methods for Integrating Stiff Differential Systems

Singla

Singh

Ramos

et al. 2022

Mathematical Problems in Engineering

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In this article, a family of one-step hybrid block methods having two intrastep points is developed for solving first-order initial value stiff differential systems that occur frequently in science and engineering. In each method of the family, an intrastep point controls the order of the main method and a second one has a control over the stability features of the method. The approach used to develop the class of A -stable methods is based on interpolation and collocation procedures. The methods exhibit hybrid nature and produce numerical solutions at several points simultaneously. These methods can also be formulated as Runge-Kutta (RK) methods. Comparisons between the RK and block formulations of the proposed methods reveal a better performance of the block formulation in terms of computational efficiency. Furthermore, the efficiency of the methods is improved when they are formulated as adaptive step-size solvers using an error-control approach. Some methods of the proposed class have been tested to solve some well-known stiff differential systems. The numerical experiments show that the proposed family of methods performs well in comparison with some of the existing methods in the scientific literature.

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A note on variable step-size formulation of a Simpson’s-type second derivative block method for solving stiff systems

Cited by 21 publications

References 8 publications

Wireless Patient Monitoring System Based on Smart Wristbands and Central user Interface Software

Wireless Patient Monitoring System Based on Smart Wristbands and Central user Interface Software

Optimizing A-stable hyperbolic fitting for time efficiency: exploring constant and variable stepsize approaches

A Family of $A$ -Stable Optimized Hybrid Block Methods for Integrating Stiff Differential Systems

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A note on variable step-size formulation of a Simpson’s-type second derivative block method for solving stiff systems

Cited by 21 publications

References 8 publications

Wireless Patient Monitoring System Based on Smart Wristbands and Central user Interface Software

Wireless Patient Monitoring System Based on Smart Wristbands and Central user Interface Software

Optimizing A-stable hyperbolic fitting for time efficiency: exploring constant and variable stepsize approaches

A Family of A -Stable Optimized Hybrid Block Methods for Integrating Stiff Differential Systems

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Product

Resources

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A Family of $A$ -Stable Optimized Hybrid Block Methods for Integrating Stiff Differential Systems