Semi-Implicit and Explicit Runge Kutta Methods for Stiff Ordinary Differential Equations

Sabawi, Younis A.; Pirdawood, Mardan A.; Khalaf, Anas D.

doi:10.1088/1742-6596/1999/1/012100

Cited by 7 publications

(6 citation statements)

References 16 publications

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“…This section focuses on the simulation of the sample paths of the mixed-weighted fractional Brownian motion and related Ornstein-Uhlenbeck process. To date, different algorithms have been used to simulate correlated Gaussian random variables (see, for instance, [21,22,30]). However, few works have studied the simulation of wfBm (see, for example, [8]).…”

Section: Numerical Simulationsmentioning

confidence: 99%

“…Consequently, new results have been established for the proposed estimator of parameter θ that are different from those that have previously been obtained for both fBm and wfBm (see Section 3). On the other hand, we used the most recent results for the numerical simulation (such as in [21][22][23][24]) to discuss the simulation of the sample paths of the mixed weighted fractional Ornstein-Uhlenbeck process.…”

Section: Introductionmentioning

confidence: 99%

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A Special Study of the Mixed Weighted Fractional Brownian Motion

et al. 2021

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In this work, we present the analysis of a mixed weighted fractional Brownian motion, defined by ηt:=Bt+ξt, where B is a Brownian motion and ξ is an independent weighted fractional Brownian motion. We also consider the parameter estimation problem for the drift parameter θ>0 in the mixed weighted fractional Ornstein–Uhlenbeck model of the form X0=0;Xt=θXtdt+dηt. Moreover, a simulation is given of sample paths of the mixed weighted fractional Ornstein–Uhlenbeck process.

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Section: Numerical Simulationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Special Study of the Mixed Weighted Fractional Brownian Motion

et al. 2021

Self Cite

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“…In addition, we propose a method to avoid the difficulties that appear when the models of ERK cell signalling pathway transfer to stiff nonlinear equations with an implicit method. This method is called Implicit -Explicit (IMEX) schemes for more details [12][13][14][15]. Consider the numerical method of the following system of stiff ordinary differential equation:…”

Section: Introductionmentioning

confidence: 99%

Model Reduction and Analysis for ERK Cell Signalling Pathway Using Implicit-Explicit Rung-Kutta Methods

Rasool

Pirdawood

Sabawi

et al. 2022

PJBAS

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Many complex cell signalling pathways and chemical reaction networks include many variables and parameters; this is sometimes a big issue for identifying critical model elements and describing the model dynamics. Therefore, model reduction approaches can be employed as a mathematical tool to reduce the number of elements. In this study, we use a new technique for model reduction: the Lumping of parameters for the simple linear chemical reaction network and the complex cell signalling pathway that is extracellular-signal-regulated kinase (ERK) pathways. Moreover, we propose a high-order and accurate method for solving stiff nonlinear ordinary differential equations. The curtail idea of this scheme is based on splitting the problem into stiff and non-stiff terms. More specifically, stiff discretization uses the implicit method, and nonlinear discretization uses the explicit method. This is consequently leading to a reduction in the computational cost of the scheme.The main aim of this study is to reduce the complex cell signalling pathway models by proposing an accurate numerical approximation Runge-Kutta method. This improves one's understanding of such behaviour of these systems and gives an accurate approximate solution. Based on the suggested technique, the simple model's parameters are minimized from 6 to 3, and the complex models from 11 to 8. Resultsshow that there is a good agreement between the original models and the simplified models.

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“…Deng et al [7] applied non-dominated solution sorting genetic algorithm (NSGA-II) to visual tracking, which well balanced the convergence and diversity of decision space and object space. In addition, Clustering Algorithm [8,9], Monarch Butterfly Optimization (MBO) [10,11], Slime Mould Algorithm (SMA) [12,13], Moth Search Algorithm (MSA) [14,15], Hunger Games Search (HGS) [16,17], Runge Kutta Method (RUN) [18,19], Colony Predation Algorithm (CPA) [20,21] and Harris Hawks Optimization (HHO) [22,23] etc., these algorithms have been applied to visual tracking and achieved great success. But up to now, there is no single algorithm that can solve all the problems perfectly.…”

Section: Introductionmentioning

confidence: 99%

Salp swarm algorithm based on golden section and adaptive and its application in target tracking

Tian¹,

Feng

Zhang

et al. 2022

IET Image Processing

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In order to solve the problem that the conventional tracker is not adapted to the abrupt motion, a tracking algorithm based on the improved salp swarm algorithm (ISSA) was proposed. Visual tracking is considered to be a process of locating the optimal position through the interaction between leaders and followers in successive images. Firstly, the adaptive mechanism of leader and follower is introduced into the original salp swarm algorithm (SSA) to balance the exploitation and exploration of the algorithm. This method can improve the accuracy and effect of tracking. Secondly, the golden‐sine algorithm was used to update the position of followers, considering that the SSA had a single spatial search mode for followers and was easy to fall into the local optimum. By comparing with 19 classical tracking algorithms, qualitative and quantitative analysis is carried out to verify the tracking effect of the proposed method. A large number of experimental results show that the algorithm proposed here has good performance in visual tracking, especially for mutation motion tracking.

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Semi-Implicit and Explicit Runge Kutta Methods for Stiff Ordinary Differential Equations

Cited by 7 publications

References 16 publications

A Special Study of the Mixed Weighted Fractional Brownian Motion

A Special Study of the Mixed Weighted Fractional Brownian Motion

Model Reduction and Analysis for ERK Cell Signalling Pathway Using Implicit-Explicit Rung-Kutta Methods

Salp swarm algorithm based on golden section and adaptive and its application in target tracking

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