Euler wavelets operational matrix of integration and its application in the calculus of variations

References

• M. Arsalani and M.A. Vali, Numerical solution of nonlinear variational problems with moving boundary conditions by using Chebyshev wavelets, Appl. Math. Sci. 5(20) (2011), pp. 947–964.
   Google Scholar
• S. Behera and S.S. Ray, An efficient numerical method based on Euler wavelets for solving fractional order pantograph Volterra delay-integro-differential equations, J. Comput. Appl. Math. 406 (2022), p. 113825.
   Web of Science ®Google Scholar
• S. Behera and S. Saha Ray, Euler wavelets method for solving fractional-order linear Volterra-Fredholm integro-differential equations with weakly singular kernels, Comput. Appl. Math. 40(6) (2021), pp. 1–30.
   Google Scholar
• R.Y. Chang and M.L. Wang, Shifted Legendre direct method for variational problems, J. Optim. Theory Appl. 39 (1983), pp. 299–307.
   Web of Science ®Google Scholar
• D. Chouhan, V. Mishra, and H.M. Srivastava, Bernoulli wavelet method for numerical solution of anomalous infiltration and diffusion modeling by nonlinear fractional differential equations of variable order, Res. Appl. Math. 10(3) (2021), p. 100146.
   Google Scholar
• I.R. Horng and J.H. Chou, Shifted Chebyshev direct method for solving variational problems, Int. J. Syst. Sci 16 (1985), pp. 855–861.
   Web of Science ®Google Scholar
• C.H. Hsiao, Haar wavelet direct method for solving variational problems, Math. Comput. Simul. 64 (2004), pp. 569–585.
   Web of Science ®Google Scholar
• E. Keshavarz, Y. Ordokhani, and M. Razzaghi, Bernoulli wavelet operational matrix of fractional order integration and its applications in solving the fractional order differential equations, Appl. Math. Model. 38(24) (2014), pp. 6038–6051.
   Web of Science ®Google Scholar
• E. Keshavarz, Y. Ordokhani, and M. Razzaghi, The Bernoulli wavelets operational matrix of integration and its applications for the solution of linear and nonlinear problems in calculus of variations, Appl. Math. Comput. 351 (2019), pp. 83–98.
   Web of Science ®Google Scholar
• A. Kheirabadi, A.M. Vaziri, and S. Effati, Solving optimal control problem using Hermite wavelet, Numer. Algebra Optim. 9(1) (2019), pp. 101–112.
   Google Scholar
• F. Khellat and S.A. Yousefi, The linear Legendre mother wavelets operational matrix of integration and its application, J. Frank. Inst. 343 (2006), pp. 181–190.
   Web of Science ®Google Scholar
• S. Mashayekhi, M. Razzaghi, and M. Wattanataweekul, Analysis of multi-delay and piecewise constant delay systems by hybrid functions approximation, Differ. Equ. Dyn. Syst. 24 (2016), pp. 1–20.
   Google Scholar
• A. Rayal and S.R. Verma, Numerical study of variational problems of moving or fixed boundary conditions by Muntz wavelets, J. Vib. Control 28(1-2) (2022), pp. 214–229.
   Web of Science ®Google Scholar
• M. Razzaghi, Fourier series direct method for variational problems, Int. J. Control 48 (1988), pp. 887–895.
   Web of Science ®Google Scholar
• M. Razzaghi and Y. Ordokhani, A rationalized haar functions method for nonlinear Fredholm-Hammerstein integral equation, Int. J. Comput. Math. 79 (2002), pp. 333–343.
   Web of Science ®Google Scholar
• M. Razzaghi and S. Yousefi, Legendre wavelets direct method for variational problems, Math. Comput. Simul. 53 (2000), pp. 185–192.
   Web of Science ®Google Scholar
• M. Razzaghi and S. Yousefi, Sine-cosine wavelets operational matrix of integration and its application in the calculus of variation, Int. J. Syst. Sci. 33 (2002), pp. 805–810.
   Web of Science ®Google Scholar
• M. Razzaghi, Y. Ordokhani, and N. Haddadi, Direct method for variational problems by using hybrid of block-pulse and Bernoulli polynomials, Rom. J. Math. Comput. Sci. 2 (2012), pp. 1–17.
   Google Scholar
• Y.X. Wang and Q.B. Fan, The second kind Chebyshev wavelet method for solving fractional differential equation, Appl. Math. Comput. 218 (2012), pp. 8592–8601.
   Web of Science ®Google Scholar
• Y.X. Wang and L. Zhu, Solving nonlinear Volterra integro-differential equations of fractional order by using Euler wavelet method, Adv. Differ. Equ. 2017(1) (2017), pp. 1–16.
   Google Scholar
• A. Yari and M. Mirnia, Direct method for solution variational problems by using Hermite polynomials, Bol. Soc. Paran. Mat. 39(6) (2021), pp. 223–237.
   Web of Science ®Google Scholar
• A. Yari and M. Mirnia, et al., Solution of optimal control problems with Payoff term and fixed state endpoint by using Bezier polynomials, Boletim Da Sociedade Paranaense De Matematica 35(1) (2017), pp. 247–267.
   Google Scholar
• L. Zhu and Q.B. Fan, Numerical solution of nonlinear fractional-order Volterra integro-differential equations by SCW, Commun. Nonlinear Sci. Numer. Simul. 18 (2013), pp. 1203–1213.
   Web of Science ®Google Scholar
• L. Zhu and Y.X. Wang, Second Chebyshev wavelet operational matrix of integration and its application in the calculus of variations, Int. J. Comput. Math. 90 (2013), pp. 2338–2352.
   Web of Science ®Google Scholar