Page 66 - IJOCTA-15-4
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MN. Khan et.al. / IJOCTA, Vol.15, No.4, pp.594-609 (2025)

             14. Baleanu D, Hajipour M, Jajarmi A. An accurate  28. Jang G-W, Kim Y Y, Choi K K. Remesh-free
                finite difference formula for the numerical solu-  shape optimization using the wavelet-Galerkin
                tion of delay-dependent fractional optimal con-   method. Int J Solids Struct. 2004;41(22-23):6465-
                trol problems. Int J Optimiz Control Theor Appl.  6483.
                2024;14(3):183-192.                           29. Liu Y, Cen Z. Daubechies wavelet meshless
             15. Abbas WS, El-wakad MT, Darwish RR. Finite el-    method for 2-D elastic problems. Tsinghua Sci
                ement modeling for two-dimensional wireless cap-  Technol. 2008;13(5):605-608.
                                                                        ¨
                sule endoscope manipulation system. Trends Adv  30. Lepik U. Solving PDEs with the aid of two-
                Sci Technol. 2025;2(1): 2.                        dimensional haar wavelets. Comput Math Appl.
             16. Masti I, Sayevand K, Jafari H. On analyzing two-  2011;61(7):1873-1879.
                dimensional fractional order brain tumor model  31. D´ıaz L A, Mart´ın M T, Vampa V. Daubechies
                based on orthonormal Bernoulli polynomials and    wavelet beam and plate finite elements. Finite El-
                Newton’s method. Int J Optimiz Control Theor      ements Anal Des. 2009;45(3):200-209.
                Appl. 2024;14(1):12-19.                       32. Khan A A, Ahsan M, Ahmad I, Alwuthay-
             17. Malagi NS, Veeresha P, Prasanna GD, Prasan-      nani M. Enhanced resolution in solving first-order
                nakumara BC, Prakasha DG. Novel approach for      nonlinear differential equations with integral con-
                nonlinear time-fractional Sharma–Tasso–Olver      dition: a high-order wavelet approach. Eur Phys
                equation using Elzaki transform. Int J Optimiz    J Spec Top. 2024;2024:1-14.
                Control Theor Appl. 2023;13(1):46-58.         33. Ahsan M, Khan A A, Dinibutun S, et al. The
             18. Erdogan U, Ozis T. A smart nonstandard fi-       haar wavelets based numerical solution of Rec-
                nite difference scheme for second order nonlin-   cati equation with integral boundary condition.
                ear boundary value problems. J Comput Phys.       Thermal Sci. 2023;27(1):93-100.
                2011;230(17):6464-6474.                       34. Shah K, Amin R, Abdeljawad T. Utiliza-
                                      ˘
                                                ˘
             19. Mukhtarov O, C¸AVUS¸OGLU S, OLGAR H. Nu-         tion of Haar wavelet collocation technique
                merical solution of one boundary value problem    for fractal-fractional order problem. Heliyon.
                using finite difference method. Turk J Math Com-  2023;9(6):e17123.
                put Sci. 2019;11:85-89.                       35. Amin R, Shah K, Awais M, Mahariq I, Nisar KS,
             20. Cheng F, Li W, Zhou Y, et al. admetSAR: a com-   Sumelka W. Existence and solution of third-order
                prehensive source and free tool for assessment of  integro-differential equations via Haar wavelet
                chemical ADMET properties. J Chem Inf Model.      method. Fractals 2023;31(02):2340037.
                2012;52(11):3099-3105.                        36. Liu X, Ahsan M, Ahmad M, et al. Applications
             21. Hoppe RH, Kieweg M. Adaptive finite element      of haar wavelet-finite difference hybrid method
                methods for mixed control-state constrained op-   and its convergence for hyperbolic nonlinear Schr
                timal control problems for elliptic boundary value  ¨ o dinger equation with energy and mass conver-
                problems. Comput Optimiz Appl. 2010;46:511-       sion. Energies 2021;14(23):7831.
                533.                                          37. Ahsan M,   Lin S,  Ahmad M, et al. A haar
             22. Hesameddini E, Riahi M. Hybrid legendre          wavelet-based scheme for finding the control pa-
                block-pulse functions method for solving par-     rameter in nonlinear inverse heat conduction
                tial differential equations with non-local inte-  equation. Open Phys. 2021;19(1): 722-734.
                gral boundary conditions. J Inform Optimiz Sci.  38. Zhou S, He Z, Chen X, Chang W. An anomaly
                2019;40(7):1391-1403.                             detection method for uav based on wavelet de-
             23. Siraj-ul-Isalm, Aziz I, Ahmad M. Numerical solu-  composition and stacked denoising autoencoder.
                tion of two-dimensional elliptic PDEs with non-   Aerospace. 2024;11(5):393.
                                                                           Sarler B. The numerical solution of
                local boundary conditions. Comput Math Appl.  39. Aziz I,  ˇ
                2015;69(3):180-205.                               second-order boundary-value problems by collo-
             24. Ooi E H, Popov V. A simplified approach for      cation method with the haar wavelets. Math Com-
                imposing the boundary conditions in the lo-       put Model. 2010;52(9-10):1577-1590.
                cal boundary integral equation method. Comput  40. Tatari M, Dehghan M. On the solution of the
                Mech. 2013;51(5):717-729.                         non-local parabolic partial differential equations
             25. Kai Y, Yin Z. On the gaussian traveling wave     via radial basis functions. Appl Math Model.,
                solution to a special kind of schr¨odinger equation  2009;33(3):1729-1738.
                with logarithmic nonlinearity. Mod Phys Lett B.,  41. Ivanauskas F, Meˇskauskas T, Sapagovas M. Sta-
                2022;36(02):2150543.                              bility of difference schemes for two-dimensional
             26. Yang Y, Li H. Neural ordinary differential equa-  parabolic equations with non-local boundary con-
                tions for robust parameter estimation in dynamic  ditions. Appl Math Comput. 2009;215(7):2716-
                systems with physical priors. Appl Soft Comput.   2732.
                2025;169:112649.                              42. Sajaviˇcius S. Stability of the weighted split-
             27. Chen Z, Wu J, Xu Y. Higher-order finite          ting finite-difference scheme for a two-dimensional
                volume methods for elliptic boundary value        parabolic equation with two nonlocal integral con-
                problems. Adv Comput Math. 2012;37(2):191-        ditions. Comput Math Appl. 2012;64(11):3485-
                253.                                              3499.
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