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Готові списки джерел за темами / Reduced Differential Transform Method (RDTM)

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Добірка наукової літератури з теми "Reduced Differential Transform Method (RDTM)"

Автор: Grafiati

Опубліковано: 7 червня 2025

Оновлено: 2 серпня 2025

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Статті в журналах з теми "Reduced Differential Transform Method (RDTM)"

1

Benhammouda, Brahim, Hector Vazquez-Leal, and Arturo Sarmiento-Reyes. "Modified Reduced Differential Transform Method for Partial Differential-Algebraic Equations." Journal of Applied Mathematics 2014 (2014): 1–9. http://dx.doi.org/10.1155/2014/279481.

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Анотація:

This work presents the application of the reduced differential transform method (RDTM) to find solutions of partial differential-algebraic equations (PDAEs). Two systems of index-two and index-three are solved to show that RDTM can provide analytical solutions for PDAEs in convergent series form. In addition, we present the posttreatment of the power series solutions with the Laplace-Padé resummation method as a useful technique to find exact solutions. The main advantage of the proposed technique is that it is based on a few straightforward steps and does not generate secular terms or depend

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2

T.R. Ramesh Rao. "A study on linear and non linear Schrodinger equations by reduced differential transform method." Malaya Journal of Matematik 4, no. 01 (2016): 59–64. http://dx.doi.org/10.26637/mjm401/008.

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Анотація:

In this paper, reduced differential transform method (RDTM) is used to obtain the exact solution of nonlinear Schrodinger equation. Compared to other existing analytical/numerical methods, RDTM is more efficient and easy to apply.

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3

Srivastava, Vineet K., Mukesh K. Awasthi, R. K. Chaurasia, and M. Tamsir. "The Telegraph Equation and Its Solution by Reduced Differential Transform Method." Modelling and Simulation in Engineering 2013 (2013): 1–6. http://dx.doi.org/10.1155/2013/746351.

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Анотація:

One-dimensional second-order hyperbolic telegraph equation was formulated using Ohm’s law and solved by a recent and reliable semianalytic method, namely, the reduced differential transform method (RDTM). Using this method, it is possible to find the exact solution or a closed approximate solution of a differential equation. Three numerical examples have been carried out in order to check the effectiveness, the accuracy, and convergence of the method. The RDTM is a powerful mathematical technique for solving wide range of problems arising in science and engineering fields.

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4

Tuan, Nguyen Minh. "A Study of Applied Reduced Differential Transform Method Using Volterra Integral Equations in Solving Partial Differential Equations." EQUATIONS 3 (October 3, 2023): 93–103. http://dx.doi.org/10.37394/232021.2023.3.11.

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Анотація:

Nowadays, integration is one of the trending fields applied in calculus, especially in partial differential equations. Researchers are contributing to support useful utilities to solve partial differential equations in many kinds of methods. In this paper, we perform an application of Volterra Integral Equations in a reduced differential transform method (we call VIE-RDTM) to find the approximate solutions of partial differential equations. The aim is to find the approximate solutions approach to the exact solutions with more general forms. We also extend some new results for basic functions a

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5

Cui, Zhoujin, Zisen Mao, Sujuan Yang, and Pinneng Yu. "Approximate Analytical Solutions of Fractional Perturbed Diffusion Equation by Reduced Differential Transform Method and the Homotopy Perturbation Method." Mathematical Problems in Engineering 2013 (2013): 1–7. http://dx.doi.org/10.1155/2013/186934.

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Анотація:

The approximate analytical solutions of differential equations with fractional time derivative are obtained with the help of a general framework of the reduced differential transform method (RDTM) and the homotopy perturbation method (HPM). RDTM technique does not require any discretization, linearization, or small perturbations and therefore it reduces significantly the numerical computation. Comparing the methodology (RDTM) with some known technique (HPM) shows that the present approach is effective and powerful. The numerical calculations are carried out when the initial conditions in the f

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6

Khalid, Aliyu Muhammad1 2. Aliyu Aliyu Isa2 3. Tiwari Sarita1 2. Sylvain Meinrad Donkeng Voumo 4*. "Application of Reduced Differential Transform Method to Solve Linear, Non-Linear Convection-Diffusion and Reaction-Diffusion Problems." MSI Journal of Multidisciplinary Research (MSIJMR) Volume 2, Issue 5 (2025): 55–64. https://doi.org/10.5281/zenodo.15372549.

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Анотація:

Convection-diffusion and reaction-diffusion equations are fundamental in describing various physical phenomena, yet their solution, particularly for nonlinear cases, often presents significant mathematical challenges. This study investigates the application of the Reduced Differential Transform Method (RDTM) to obtain analytical solutions for both linear and nonlinear convection-diffusion and reaction-diffusion problems. The RDTM, derived from power series expansion, was systematically applied to four illustrative examples: two linear convection-diffusion equations and two nonlinear reaction-d

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7

Abdul Rahman Farhan Sabdin, Che Haziqah Che Hussin, Jumat Sulaiman, and Arif Mandangan. "Multistep Reduced Differential Transform Method in Solving Nonlinear Schrodinger Equations." Journal of Advanced Research in Applied Sciences and Engineering Technology 44, no. 2 (2024): 112–23. http://dx.doi.org/10.37934/araset.44.2.112123.

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Анотація:

This paper obtains semi-analytical solutions for the nonlinear Schrodinger equations (NLSEs) using the multistep reduced differential transform method (MsRDTM). The implemented method yields an analytical approximate solution over a longer time frame, in which the method applied is treated as an algorithm in a sequence of small sub-division of intervals of identical length compared to the traditional reduced differential transform method (RDTM). Excluding the need of perturbation, linearization, or discretization, this method offers the benefit and reliability of the multistep algorithm. The o

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8

Abazari, Reza, and Adem Kılıçman. "Numerical Study of Two-Dimensional Volterra Integral Equations by RDTM and Comparison with DTM." Abstract and Applied Analysis 2013 (2013): 1–10. http://dx.doi.org/10.1155/2013/929478.

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Анотація:

The two-dimensional Volterra integral equations are solved using more recent semianalytic method, the reduced differential transform method (the so-called RDTM), and compared with the differential transform method (DTM). The concepts of DTM and RDTM are briefly explained, and their application to the two-dimensional Volterra integral equations is studied. The results obtained by DTM and RDTM together are compared with exact solution. As an important result, it is depicted that the RDTM results are more accurate in comparison with those obtained by DTM applied to the same Volterra integral equa

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9

Osman, Mawia, Yonghui Xia, Muhammad Marwan, and Omer Abdalrhman Omer. "Novel Approaches for Solving Fuzzy Fractional Partial Differential Equations." Fractal and Fractional 6, no. 11 (2022): 656. http://dx.doi.org/10.3390/fractalfract6110656.

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Анотація:

In this paper, we present a comparison of several important methods to solve fuzzy partial differential equations (PDEs). These methods include the fuzzy reduced differential transform method (RDTM), fuzzy Adomian decomposition method (ADM), fuzzy Homotopy perturbation method (HPM), and fuzzy Homotopy analysis method (HAM). A distinguishing practical feature of these techniques is administered without the need to use discretion or restricted assumptions. Moreover, we investigate the fuzzy (n+1)-dimensional fractional RDTM to obtain the solutions of fuzzy fractional PDEs. The much more distinct

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10

Arslan, Derya. "The Comparison Study of Hybrid Method with RDTM for Solving Rosenau-Hyman Equation." Applied Mathematics and Nonlinear Sciences 5, no. 1 (2020): 267–74. http://dx.doi.org/10.2478/amns.2020.1.00024.

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AbstractIn this paper, the hybrid method (differential transform and finite difference methods) and the RDTM (reduced differential transform method) are implemented to solve Rosenau-Hyman equation. These methods give the desired accurate results in only a few terms and the approach procedure is rather simple and effective. An experiment is given to demonstrate the efficiency and reliability of these presented methods. The obtained numerical results are compared with each other and with exact solution. It seems that the results of the hybrid method and the RDTM show good performance as the othe

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Більше джерел

Частини книг з теми "Reduced Differential Transform Method (RDTM)"

1

Saha Ray, Santanu. "New Techniques on Fractional Reduced Differential Transform Method." In Nonlinear Differential Equations in Physics. Springer Singapore, 2019. http://dx.doi.org/10.1007/978-981-15-1656-6_7.

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2

Gandhi, Hemant, Amit Tomar, and Dimple Singh. "A Predicted Mathematical Cancer Tumor Growth Model of Brain and Its Analytical Solution by Reduced Differential Transform Method." In Advances in Intelligent Systems and Computing. Springer Singapore, 2020. http://dx.doi.org/10.1007/978-981-15-5414-8_17.

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3

Sharma, Aruna, and Amit K. Parikh. "Semi-analytic Solution of Co-current Imbibition Phenomenon in Inclined Heterogeneous Porous Medium Using Reduced Differential Transform Method." In Innovations in Sustainable Technologies and Computing. Springer Nature Singapore, 2025. https://doi.org/10.1007/978-981-97-6794-6_31.

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4

SINGH, PRABAL PRATAP, OMENDRA SINGH, and SEEMA RAGHAV. "REDUCED DIFFERENTIAL TRANSFORM METHOD FOR TIME FRACTIONAL NONLINEAR PDES: MATHEMATICAL FRAMEWORK AND COMPUTATIONAL ASPECTS." In Recent Advances in Applied Science & Technology towards Sustainable Environment. NOBLE SCIENCE PRESS, 2024. https://doi.org/10.52458/9788197112492.nsp.2024.eb.ch-16.

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Анотація:

Because of its computing efficiency, precision, and relative simplicity, the Reduced Differential Transform Method (RDTM) has become a powerful analytical tool for solving many types of partial differential equations (PDEs). Our focus here is on time fractional nonlinear PDEs, a large and important class of mathematical models, and how RDTM may be applied to solve them. Traditional solution methods are challenged by the complicated behaviour of these equations, which emerge in different scientific areas including physics, engineering, and biology. This study lays out a full mathematical scheme

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5

Pujari, Puspalata, and Babita Majhi. "Application of Natured-Inspired Technique to Odia Handwritten Numeral Recognition." In Advances in Computational Intelligence and Robotics. IGI Global, 2018. http://dx.doi.org/10.4018/978-1-5225-2857-9.ch019.

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Анотація:

In this chapter an effort has been made to develop a hybrid system using functional link artificial neural network (FLANN) and differential evolution (DE) for effective recognition of Odia handwritten numerals. The S-transform (ST) is chosen for feature extraction from handwritten numerals and these are further reduced by using principal component analysis (PCA). After reduction of feature the reduced features are applied to FLANN model for recognition of each numeral. Further differential evolution algorithm (DE) is used for the optimization of weights of FLANN classifier. For performance com

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Тези доповідей конференцій з теми "Reduced Differential Transform Method (RDTM)"

1

Fadugba, Sunday Emmanuel, Adaobi Mmachukwu Udoye, Samuel Chiabom Zelibe, et al. "Reduced differential transform method for Solving Black-Scholes European options model in the sense of powered modified log-payoff function." In 2024 International Conference on Science, Engineering and Business for Driving Sustainable Development Goals (SEB4SDG). IEEE, 2024. http://dx.doi.org/10.1109/seb4sdg60871.2024.10629788.

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2

Servi, Sema, Yildiray Keskin, and Galip Oturanç. "Reduced differential transform method for improved Boussinesq equation." In PROCEEDINGS OF THE INTERNATIONAL CONFERENCE ON NUMERICAL ANALYSIS AND APPLIED MATHEMATICS 2014 (ICNAAM-2014). AIP Publishing LLC, 2015. http://dx.doi.org/10.1063/1.4912601.

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3

Sabdin, Abdul Rahman Farhan, Che Haziqah Che Hussin, Jumat Sulaiman, and Arif Mandangan. "Reduced differential transform method in solving Nonlinear Schrodinger Equations." In 5TH INTERNATIONAL CONFERENCE ON MATHEMATICAL SCIENCES (ICMS5). AIP Publishing, 2024. http://dx.doi.org/10.1063/5.0228534.

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4

Fadugba, Sunday Emmanuel, Matthew Olanrewaju Oluwayemi, Adedoyin Olayinka Ajayi, Olanrewaju Faweya, Joseph Temitayo Okunlola, and Malesela Kekana. "Fractional Reduced Differential Transform Method for Solving Fractional Order Measles Model." In 2023 International Conference on Science, Engineering and Business for Sustainable Development Goals (SEB-SDG). IEEE, 2023. http://dx.doi.org/10.1109/seb-sdg57117.2023.10124484.

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5

Acan, Omer, and Yıldıray Keskin. "Approximate solution of Kuramoto–Sivashinsky equation using reduced differential transform method." In PROCEEDINGS OF THE INTERNATIONAL CONFERENCE ON NUMERICAL ANALYSIS AND APPLIED MATHEMATICS 2014 (ICNAAM-2014). AIP Publishing LLC, 2015. http://dx.doi.org/10.1063/1.4912680.

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6

Appadu, Appanah Rao, and Abey Sherif Kelil. "Solution of 3D linearized KdV equation using reduced differential transform method." In INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2020. AIP Publishing, 2022. http://dx.doi.org/10.1063/5.0081390.

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7

Saeed, Rostam K., and Andam A. Mustafa. "Numerical solution of Fisher–KPP equation by using reduced differential transform method." In 6TH INTERNATIONAL CONFERENCE AND WORKSHOPS ON BASIC AND APPLIED SCIENCES. Author(s), 2017. http://dx.doi.org/10.1063/1.5004322.

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8

Al-Rozbayani, Abdulghafor M., and Abdulbaset H. Shammar. "Applied reduced differential transform method to the Wu-Zhang equation in (1+1)-dimensional." In INTERNATIONAL CONFERENCE OF COMPUTATIONAL METHODS IN SCIENCES AND ENGINEERING ICCMSE 2021. AIP Publishing, 2023. http://dx.doi.org/10.1063/5.0114833.

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9

Hussin, Che Haziqah Che, Ahmad Izani Md Ismail, Adem Kilicman, and Amirah Azmi. "Approximate analytical solutions of fractional nonlinear Schrodinger equations using multistep modified reduced differential transform method." In PROCEEDINGS OF THE INTERNATIONAL CONFERENCE ON MATHEMATICAL SCIENCES AND TECHNOLOGY 2018 (MATHTECH2018): Innovative Technologies for Mathematics & Mathematics for Technological Innovation. AIP Publishing, 2019. http://dx.doi.org/10.1063/1.5136435.

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10

Acan, Omer, and Yıldıray Keskin. "Reduced differential transform method for (2+1) dimensional type of the Zakharov–Kuznetsov ZK(n,n) equations." In PROCEEDINGS OF THE INTERNATIONAL CONFERENCE ON NUMERICAL ANALYSIS AND APPLIED MATHEMATICS 2014 (ICNAAM-2014). AIP Publishing LLC, 2015. http://dx.doi.org/10.1063/1.4912604.

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