Numerical inversion method for the Laplace transform based on Boubaker polynomials operational matrix
Abstract
We investigate through this research the numerical inversion technique for the Laplace transforms cooperated by the integration Boubaker polynomials operational matrix. The efficiency of the presented approach is demonstrated by solving some differential equations. Also, this technique is combined with the standard Laplace Homotopy Perturbation Method. The numerical results highlight that there is a very good agreement between the estimated solutions with exact solutions.
References
- 1. , Numerical inversion of Laplace transform using Haar wavelet operational matrices, IEEE Trans. Circuit. Syst. I 48 :120–122, 2001. Crossref, Web of Science, Google Scholar
- 2. , Numerical method for inverse Laplace transform with Haar wavelet operational matrix, Malays. J. Fundam. Appl. Sci. 8 :182–188, 2012. Google Scholar
- 3. , Direct method to solve Volterra integral equation of the first kind using operational matrix with block-pulse functions, J. Comput. Appl. Math. 220 :51–57, 2008. Crossref, Web of Science, Google Scholar
- 4. , Numerical inverse Laplace transform based on Bernoulli polynomials operational matrix for solving nonlinear differential equations, Res. Phys. 16 :102836, 2020. Google Scholar
- 5. , Numerical inversion of Laplace transform based on Bernstein operational matrix, Math. Methods Appl. Sci. 41 :9231–9243, 2018. Crossref, Web of Science, Google Scholar
- 6. , Numerical inverse Laplace transform for solving a class of fractional differential equations, Symmetry 11 :1–20, 2019. Crossref, Web of Science, Google Scholar
- 7. , Application of Laguerre matrix polynomials to the numerical inversion of Laplace transforms of matrix functions, Appl. Math. Lett. 24 :1527–1532, 2011. Crossref, Web of Science, Google Scholar
- 8. , Chebyshev Polynomial based numerical inverse laplace transform solutions of linear volterra integral and integro-differential equations, Am. Res. J. Math. 1 :22–32, 2015. Google Scholar
- 9. , Herd behavior in a predator–prey model with spatial diffusion bifurcation analysis and Turing instability, J. Appl. Math. Comput. 58(1–2) :125–149, 2017. Crossref, Web of Science, Google Scholar
- 10. , Impact of prey herd shape on the predator–prey interaction, Chaos Solitons Fractals 120 :139–148, 2019. Crossref, Web of Science, Google Scholar
- 11. , Spatiotemporal patterns induced by cross-diffusion in predator-prey model with prey herd shape effect, Int. J. Biomath. 13(4) :2050030, 2020, https//doi.org/10.1142/S1793524520500308. Link, Web of Science, Google Scholar
- 12. , Impact of predation in the spread of an infectious disease with time fractional derivative and social behavior, Int. J. Model. Simul. Scientific Comput. 12(4) :2150023, 2020. Link, Web of Science, Google Scholar
- 13. , Coronavirus pandemic A predictive analysis of the peak outbreak epidemic in South Africa, Turkey, and Brazil, Chaos, Solitons Fractals 138 :109971, 2020. Crossref, Web of Science, Google Scholar
- 14. , Age-structured Modeling of COVID-19 Epidemic in the USA, UAE and Algeria, Alexandria Engin. J. 60(1) :401–411, 2020, https//doi.org/10.1016/j.aej.2020.08.053. Crossref, Web of Science, Google Scholar
- 15. , Modeling the impact of unreported cases of the COVID-19 in the North African countries, Biology 9(11) :373, 2020, https://doi.org/10.3390/biology9110373. Crossref, Web of Science, Google Scholar
- 16. , Global dynamics of an SEIR model with two age structures and a nonlinear incidence, Acta Appl. Math. 2020, https://doi.org/10.1007/s10440-020-00369-z. Web of Science, Google Scholar
- 17. , A study of behaviour for immune and tumor cells in immunogenetic tumour model with non-singular fractional derivative, Chaos Solitons Fractals 133 :109619, 2020. Crossref, Web of Science, Google Scholar
- 18. , A Heroin epidemic model very general nonlinear incidence, treat-age, and global stability, Acta Appl. Math. 152(1) :171–194, 2017. Crossref, Web of Science, Google Scholar
- 19. , Global threshold dynamics of an age structured alcoholism model, Int. J. Biomath. 14(3) :2150013, 2020, https://doi.org/10.1142/S1793524521500133. Link, Web of Science, Google Scholar
- 20. , Comparative numerical study of single and two-phase models of nano-fluid heat transfer in wavy channel, Appl. Math. Mech. 35 :831–848, 2014. Crossref, Web of Science, Google Scholar
- 21. , A new analytical modelling for fractional telegraph equation via Laplace transform, Appl. Math. Model. 38(13) :3154–3163, 2014. Crossref, Web of Science, Google Scholar
- 22. , Two analytical methods for time-fractional nonlinear coupled Boussinesq-Burger’s equations arise in propagation of shallow water waves, Nonlinear Dyn. 85 :699-715, 2016. Crossref, Web of Science, Google Scholar
- 23. , New analytical method for gas dynamics equation arising in shock fronts, Comput. Phys. Commun. 185(7) :1947–1954, 2014. Crossref, Web of Science, Google Scholar
- 24. , Similarities in a fifth-order evolution equation with and with no singular kernel, Chaos Solitons Fractals 30 :109467, 2020. Crossref, Web of Science, Google Scholar
- 25. , Analytical solution of fractional Navier–Stokes equation by using modified Laplace decomposition method, Ain Shams Eng. J. 5(2) :569–574, 2014. Crossref, Google Scholar
- 26. , An analysis for heat equations arises in diffusion process using new Yang–Abdel–Aty–Cattani fractional operator, Math. Methods Appl. Sci. 43(9) :6062–6080, 2020. Crossref, Web of Science, Google Scholar
- 27. , A study of fractional Lotka–Volterra population model using Haar wavelet and Adams–Bashforth–Moulton methods, Math. Methods Appl. Sci. 43(8) :5564–5578, 2020. Crossref, Web of Science, Google Scholar
- 28. , On modified Boubaker polynomials: Some differential and analytical properties of the new polynomial issued from an attempt for solving bi-varied heat equation, Trends Appl. Sci. Res. 2 :540–544, 2007. Crossref, Google Scholar
- 29. , Some new features of the Boubaker polynomials expansion scheme BPES, Math. Notes 87 :175–178, 2010. Crossref, Web of Science, Google Scholar
- 30. , Some new properties of the applied-physics related Boubaker polynomials, Differ. Equ. Control Process. 1 :7–19, 2009. Google Scholar
- 31. , Boubaker polynomials collocation approach for solving systems of nonlinear Volterra–Fredholm integral equations, J. Taibah Univ. Sci. 11 :1182–1199, 2017. Crossref, Web of Science, Google Scholar
- 32. , Numerical solutions of multi-order fractional differential equations by Boubaker polynomials, Open Phys. 14(1) :28–33, 2016. Crossref, Web of Science, Google Scholar
- 33. , Numerical solution of nonlinear Volterra–Fredholm integral equations using hybrid of block-pulse functions and Taylor series, Alex. Eng. J. 52 :551–555, 2013. Crossref, Google Scholar
- 34. , Numerical Methods for Laplace Transform Inversion (Springer, New York, USA, 2007). Google Scholar
- 35. , The Boubaker polynomials and their application to solve fractional optimal control problems, Nonlinear Dyn. 88(2) :1013–1026, 2016. Crossref, Web of Science, Google Scholar
- 36. , Homotopy perturbation method with Laplace Transform (LT-HPM) for solving Lane–Emden type differential equations, Springer Plus 5 :1859, 2016. Crossref, Google Scholar
- 37. , Homotopy perturbation technique, Comput. Methods Appl. Mech. Eng. 178(3) :257–262, 1999. Crossref, Web of Science, Google Scholar
Remember to check out the Most Cited Articles! |
---|
Check out our handbook collection in computer science! |