Generic symbolic parameters varying systems frameworks versus other techniques: Returning back to the roots

Dorrah, Hassen T.; Gabr, Walaa Ibrahim; El-Sayed, Mohamed

doi:10.1016/j.aej.2017.11.021

Cited by 9 publications

(4 citation statements)

References 10 publications

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“…However, in some cases, using symbolic computations can lead to slower execution times depending on the program used and the process [4][5][6]. Symbolic computation has been used and proposed for solving many different problems [7][8][9][10][11].…”

Section: Introductionmentioning

confidence: 99%

Comparison of Symbolic Computations for Solving Linear Delay Differential Equations Using the Laplace Transform Method

Sherman

Kerr

González-Parra

2022

MCA

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In this paper, we focus on investigating the performance of the mathematical software program Maple and the programming language MATLAB when using these respective platforms to compute the method of steps (MoS) and the Laplace transform (LT) solutions for neutral and retarded linear delay differential equations (DDEs). We computed the analytical solutions that are obtained by using the Laplace transform method and the method of steps. The accuracy of the Laplace method solutions was determined (or assessed) by comparing them with those obtained by the method of steps. The Laplace transform method requires, among other mathematical tools, the use of the Cauchy residue theorem and the computation of an infinite series. Symbolic computation facilitates the whole process, providing solutions that would be unmanageable by hand. The results obtained here emphasize the fact that symbolic computation is a powerful tool for computing analytical solutions for linear delay differential equations. From a computational viewpoint, we found that the computation time is dependent on the complexity of the history function, the number of terms used in the LT solution, the number of intervals used in the MoS solution, and the parameters of the DDE. Finally, we found that, for linear non-neutral DDEs, MATLAB symbolic computations were faster than Maple. However, for linear neutral DDEs, which are often more complex to solve, Maple was faster. Regarding the accuracy of the LT solutions, Maple was, in a few cases, slightly better than MATLAB, but both were highly reliable.

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Section: Introductionmentioning

confidence: 99%

Comparison of Symbolic Computations for Solving Linear Delay Differential Equations Using the Laplace Transform Method

Sherman

Kerr

González-Parra

2022

MCA

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“…It relies on partitioning a large matrix into compatible smaller sections referred to as sub-matrices or blocks. Hence, manipulations can be performed on the smaller blocks which in turn leads to significant computational benefits [21]. The complete flow chart of the proposed symbolicbased technique for solving complex state space models is depicted in Figure 1.…”

Section: The Proposed Techniquementioning

confidence: 99%

Fully symbolic-based technique for solving complex state-space control systems

Abd-AlRahem

Elhadidy

Elserafi

et al. 2021

IJECE

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Despite the superiority of symbolic approaches over the purely numerical approaches in many aspects, it does not receive the proper attention due to its significant complexity, high resources requirement and long drawn time which even grows significantly with the increase of model dimensions. However, its merits deserve every attempt to overcome the difficulties being faced. In this paper, a fully generic symbolic-based technique is proposed to deal with complex state space control problems. In this technique, depending on the model dimension if exceeds a predefined limit, the state space is solved using the partitioned matrices theory and block wise inversion formula. Experimental results demonstrate that the proposed technique overcomes all the previously mentioned barriers and gives the same results when compared to numerical methods (Simulink). Moreover, it can be used to gain useful information about the system itself, provides an indication of which parameters are more important and reveals the sensitivity of system model to single parameter variations.

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“…Both equations (3) and (1), and also (4) and (2) are analogous but physically are representing flows in backward order.…”

Section: B One-step Flow Disaggregation Modular Representationmentioning

confidence: 99%

“…The application of symbolic-based modeling and analysis of natural and man-made systems has been recently more emphasized [3]. The implementation of such symbolic-based mathematical approach has been extended in many classes of systems in areas of engineering, automatic control, life sciences, utilities operational networks, .…”

Section: Introductionmentioning

confidence: 99%

A New Symbolic-Based Flow Aggregation and Disaggregation Modular Approach for Tree-shaped Networks

Gabr

Dorrah

2020

IEEE Access

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This paper presents the representation and modeling of real-life tree-shaped natural and manmade networks. It is shown that the tree-shaped networks could be composed of two entities of different functionalities that can operate separately or jointly. The first entity is the feet/head aggregation networks, while the second entity is the head/feet disaggregation networks. Each entity is represented with the same symbolic-based modular model expressions. Moreover, it is illustrated that the aggregation entity network can be mapped through a mirroring type process to an analogous disaggregation entity network and vice versa. The suggested technique is demonstrated by an application of the modeling of 20-nodes reallife tree-shaped irrigation network. The paper also addresses simultaneously the analogy between natural plant tree morphology and natural/man-made operational network of both the aggregation or disaggregation types. It is highlighted that such analogy with the natural tree system could help in future schematizing of stages of operational networks expansion in the most efficient way as learnt from nature and in building advanced generations of operational networks. Furthermore, it is pointed out that the new approach has unlimited scope of real-life applications in engineering/technology such as electric generation, water basins, sewage, agriculture drainage, highway transportation ..etc. networks for the aggregation entity, and electric distribution, irrigation, oil, gas, potable water, roads transport, ..etc. networks for the disaggregation entity. In all respects, the paper has succeeded within the area of tree-shaped networks in crossing the boundaries between the Science of Botany and Engineering/technology (and vice versa) and to create new common areas of important shared interests of great benefits to these disciplines and the science world as a whole. Finally, the new notion of crossing boundaries between sciences can also be extended to and among many other sciences themselves dealing with tree-shaped systems. INDEX TERMS Crossing the boundaries between sciences, ecology and hydrology, evolutionary systems, feet/head aggregation networks, head/feet disaggregation networks, life sciences, medicine and biology, multi-step modular modeling, real-life natural and man-made operational networks, engineering and technology, symbolic-based mathematical modeling, the tree of life, the science of botany, tree-shaped morphology, water and energy.

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Generic symbolic parameters varying systems frameworks versus other techniques: Returning back to the roots

Cited by 9 publications

References 10 publications

Comparison of Symbolic Computations for Solving Linear Delay Differential Equations Using the Laplace Transform Method

Comparison of Symbolic Computations for Solving Linear Delay Differential Equations Using the Laplace Transform Method

Fully symbolic-based technique for solving complex state-space control systems

A New Symbolic-Based Flow Aggregation and Disaggregation Modular Approach for Tree-shaped Networks

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