A new third order convergent numerical solver for continuous dynamical systems

Qureshi, Sania; Yusuf, Abdullahi

doi:10.1016/j.jksus.2019.11.035

Cited by 18 publications

(8 citation statements)

References 15 publications

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“…As the classical approaches of mathematical models do not determine high degree of accuracy to model these diseases, fractional differential equations were introduced to handle such problems, which have many applications in applied fields like production problems, optimization problems, artificial intelligence, medical diagnoses, robotics, cosmology, and many more. Fractional differential equations are used in mathematical models of biological phenomena during the last few decades [5] , [6] , [7] , [8] , [9] , [10] , [11] , [12] . One of the infectious diseases is COVID-19 caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2).…”

Section: Introductionmentioning

confidence: 99%

Mathematical analysis of SIRD model of COVID-19 with Caputo fractional derivative based on real data

et al. 2021

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Section: Introductionmentioning

confidence: 99%

Mathematical analysis of SIRD model of COVID-19 with Caputo fractional derivative based on real data

et al. 2021

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“…The modeling of FPDEs, whether they are with respect to time or space, is more convergent, and many natural phenomena are accurately described by them. The researchers in the fields of anomalous diffusion, dielectric polarization, control theory, and other problems of physical phenomena are interested in FPDEs [4][5][6][7][8][9][10]. Since the fractional order of the derivative works more accurately than integer order in describing the properties related to hereditary and where the future state is influenced by the past state, FPDEs give the highest contribution to explaining such types of systems.…”

Section: Introductionmentioning

confidence: 99%

A New Modified Technique of Adomian Decomposition Method for Fractional Diffusion Equations with Initial-Boundary Conditions

Masood

Hajira

Khan

et al. 2022

Journal of Function Spaces

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In general, solving fractional partial differential equations either numerically or analytically is a difficult task. However, mathematicians have tried their best to make the task easy and promoted various techniques for their solutions. In this regard, a very prominent and accurate technique, which is known as the new technique of the Adomian decomposition method, is developed and presented for the solution of the initial-boundary value problem of the diffusion equation with fractional view analysis. The suggested model is an important mathematical model to study the behavior of degrees of memory in diffusing materials. Some important results for the given model at different fractional orders of the derivatives are achieved. Graphs show the obtained results to confirm the accuracy and validity of the suggested technique. These results are in good contact with the physical dynamics of the targeted problems. The obtained results for both fractional and integer orders problems are explained through graphs and tables. Tables and graphs support the physical behavior of each problem and the best of physical analysis. From the results, it is concluded that as the fractional order derivative is changed, the graphs or paths of dynamics are also changed. Therefore, we now choose the best solution or dynamic of the problem at a particular derivative order. It is analyzed that the present technique is one of the best techniques to handle the solutions of fractional partial differential equations having initial and boundary conditions (BCs), which are very rare in literature. Furthermore, a small number of calculations are done to achieve a very high rate of convergence, which is the novelty of the present research work. The proposed method provides the series solution with twice recursive formulae to increase the desired accuracy and is preferred among the best techniques to find the solution of fractional partial differential equations with mixed initials and BCs.

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“…One mathematical model is different from another in many respects, such as physical interpretation of the model, characteristics of parameters contained therein, and given conditions. Therefore, one numerical technique is not sufficient to serve the general purpose, thereby leading to have much research works on developing new numerical techniques [18][19][20][21][22]. These are the techniques suitable for a particular set of problems, and this search continues to the day.…”

Section: Introductionmentioning

confidence: 99%

A New Nonlinear Hybrid Technique with fixed and adaptive step-size approaches

Soomro¹

2022

Sigma J Eng Nat Sci - Sigma Müh Fen Bil Derg

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Linear and nonlinear numerical techniques are the most popular techniques for finding approximate solutions to initial value problems in numerous scientific fields. Due to the substantial importance of ordinary differential equations, an attempt has been made in the present research study to obtain a new nonlinear hybrid technique based upon contraharmonic and harmonic means having fourth-order accuracy. Theoretical analysis in terms of consistency, stability, asymptotic errors (local and global truncation errors), and convergence has also been carried out. The newly formulated technique is compared with some existing techniques having the same characteristics and observed to be much better because of errors, CPU time, and stability region. The adaptive step-size approach improves the performance of the proposed technique, and strategies to control the errors are developed. Some numerical experiments for scalar and vector initial value problems, including logistic growth, sinusoidal and industrial Robot Arm systems, are presented to show better performance of the proposed technique.

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A new third order convergent numerical solver for continuous dynamical systems

Cited by 18 publications

References 15 publications

Mathematical analysis of SIRD model of COVID-19 with Caputo fractional derivative based on real data

Mathematical analysis of SIRD model of COVID-19 with Caputo fractional derivative based on real data

A New Modified Technique of Adomian Decomposition Method for Fractional Diffusion Equations with Initial-Boundary Conditions

A New Nonlinear Hybrid Technique with fixed and adaptive step-size approaches

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