THERMAL SCIENCE

International Scientific Journal

Authors of this Paper

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Xian-Yong Liu

,

Yan-Ping Liu

,

Zeng-Wen Wu

COMPUTER SIMULATION OF PANTOGRAPH DELAY DIFFERENTIAL EQUATIONS

ABSTRACT
Ritz method is widely used in variational theory to search for an approximate solution. This paper suggests a Ritz-like method for integral equations with an emphasis of pantograph delay equations. The unknown parameters involved in the trial solution can be determined by balancing the fundamental terms.
KEYWORDS
Integral equation, series solution, variational principle, Pantograph delay differential equation
PAPER SUBMITTED: 2020-02-20
PAPER REVISED: 2020-06-01
PAPER ACCEPTED: 2020-06-02
PUBLISHED ONLINE: 2021-01-31
DOI REFERENCE: https://doi.org/10.2298/TSCI200220037L
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2021, VOLUME 25, ISSUE Issue 2, PAGES [1381 - 1385]
REFERENCES
  1. Shahgholian, D., et al., Buckling Analyses of Functionally Graded Graphene-Reinforced Porous Cylindrical Shell Using the Rayleigh-Ritz Method, Acta Mechanica, 231 (2020), Feb., pp. 1887-1902
  2. He, J. H., Generalized Variational Principles for Buckling Analysis of Circular Cylinders, Acta Mechanica, 231 (2020), Dec., pp. 899-906
  3. He, J. H., A Fractal Variational Theory for 1-D Compressible Flow in a Microgravity Space, Fractals, 28 (2020), 02, 2050024
  4. He, J.-H., Variational Principle and Periodic Solution of the Kundu-Mukherjee-Naskar Equation, Results in Physics, 17 (2020), June, 103031
  5. He, J. H., Lagrange Crisis and Generalized Variational Principle for 3-D Unsteady Flow, International Journal of Numerical Methods for Heat and Fluid-Flow, 30 (2019), 3, pp. 1189-1196
  6. He, J. H., Sun, C. A., Variational Principle for a Thin Film Equation, Journal of Mathematical Chemistry, 57 (2019), 9, pp. 2075-2081
  7. He, J. H., Ain, Q. T., New Promises and Future Challenges of Fractal Calculus: From Two-Scale Thermodynamics to Fractal Variational Principle, Thermal Science, 24 (2020), 2A, pp. 659-681
  8. He, J. H., Variational Principle and Periodic Solution of the Kundu-Mukherjee-Naskar Equation, Results in Physics, 17 (2020), 103031
  9. He, C.H., et al., Taylor Series Solution for Fractal Bratu-Type Equation Arising in eElectrospinning Process, Fractals, 28 (2020), 1, 2050011
  10. He, J. H., A Simple Approach to 1-D Convection-Diffusion Equation and Its Fractional Modification for E Reaction Arising in Rotating Disk Electrodes, Journal of Electroanalytical Chemistry, 854 (2019), 113565
  11. He, J. H., Ji, F. Y., Taylor Series Solution for Lane-Emden Equation, Journal of Mathematical Chemistry, 57 (2019), 8, pp. 1932-1934
  12. He, J. H., The Simplest Approach to Non-Linear Oscillators, Results in Physics, 15 (2019), 102546
  13. He, J. H., Taylor Series Solution for a Third Order Boundary Value Problem Arising in Architectural Engineering, Ain Shams Engineering Journal, On-line first, doi.org/10.1016/j.asej.2020.01.016, 2020
  14. He, J. H., Latifizadeh, H., A General Numerical Algorithm for Non-Linear Differential Equations by the Variational Iteration Method, International Journal of Numerical Methods for Heat and Fluid-Flow, 30 (2020), 11, pp. 4797-4810
  15. Ji, F. Y., et al., A Fractal Boussinesq Equation for Non-Linear Transverse Vibration of a Nanofiber-Reinforced Concrete Pillar, Applied Mathematical Modelling, 82 (2020), June, pp. 437-448
  16. He, J. H., A Short Review on Analytical Methods for to a Fully Fourth Order Non-Linear Integral Boundary Value Problem with Fractal Derivatives, International Journal of Numerical Methods for Heat and Fluid-Flow, 30 (2020), 11, pp. 4933-4943
  17. He, J. H., Jin, X., A Short Review on Analytical Methods for the Capillary Oscillator in a Nanoscale Deformable Tube, Mathematical Methods in the Applied Sciences, On-line first, dx.doi.org/10.1002/ mma.6321, 2020
  18. He, C. H., et al., Fangzhu, An Ancient Chinese Nanotechnology for Water Collection from Air, History, Mathematical Insight, Promises and Challenges, Mathematical Methods in the Applied Sciences, (2020), On-line first, doi.org/10.1002/mma.6384, 2020
  19. Ahmad, H., Khan, T. A., Variational Iteration Algorithm-I with an Auxiliary Parameter for Wave-Like Vibration Equations, Journal of Low Frequency Noise Vibration and Active Control, 38 (2019), 3-4, pp. 1113-1124
  20. Wei, C. F., Application of the Homotopy Perturbation Method for Solving Fractional Lane-Emden Type Equation, Thermal Science, 23 (2019), 4, pp. 2237-2244
  21. Yang, Y. J., Wang, S. Q., A Local Fractional Homotopy Perturbation Method for Solving the Local Fractional Korteweg-de Vries Equations with Non-Homogeneous Term, Thermal Science, 23 (2019), 3A, pp. 1495-1501
  22. Kuang, W. X., et al. Homotopy Perturbation Method with an Auxiliary Term for the Optimal Design of a Tangent Non-Linear Packaging System, Journal of Low Frequency Noise Vibration and Active Control, 38 (2019), 3-4, pp. 1075-1080
  23. Pasha, S. A., et al., The Modified Homotopy Perturbation Method with an Auxiliary Term for the Non-Linear Oscillator with Discontinuity, Journal of Low Frequency Noise Vibration and Active Control, 38 (2019), 3-4, pp. 1363-1373
  24. Li, X. X., He, C. H., Homotopy Perturbation Method Coupled with the Enhanced Perturbation Method, Journal of Low Frequency Noise Vibration and Active Control, 38 (2019), 3-4, pp. 1399-1403
  25. Yu, D. N., et al., Homotopy Perturbation Method with an Auxiliary Parameter for Non-Linear Oscillators, Journal of Low Frequency Noise Vibration and Active Control, 38 (2019), 3-4, ppp. 1540-1554
  26. He, J. H., The Simpler, the Better: Analytical Methods for Non-Linear Oscillators and Fractional Oscillators, Journal of Low Frequency Noise Vibration and Active Control, 38 (2019), 3-4, pp. 1252-1260
  27. Bahgat, M. S. M., Approximate Analytical Solution of the Linear and Non-Linear Multi-Pantograph Delay Differential Equations, Physica Scripta, 95 (2020), 055219
  28. Sedaghat, S., et al., Analysis of Spectral Method for Neutral Multi-Pantograph Equations, Iranian Journal of Science and Technology Transaction A-Science, 43 (2019), A5, pp. 2261-2268
  29. He, J.-H., Fractal Calculus and its Geometrical Explanation, Results in Physics, 10 (2018), Sept., pp. 272-276
  30. Ain, Q. T., He, J.-H., On Two-Scale Dimension and its Applications, Thermal Science, 23 (2019) , 3, pp. 1707-1712
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Computer simulation of pantograph delay differential equations

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