Abstract
The Legendre wavelet collocation method (LWCM) is suggested in this study for solving high-order boundary value problems numerically. Eighth, tenth, and twelfth-order examples are used as test problems to ensure that the technique is efficient and accurate. In comparison to other approaches, the numerical results obtained using LWCM demonstrate that the method's accuracy is very good. The results indicate that the method requires less computational effort to achieve better results.
Highlights
The researchers are targeting ordinary differentials equation because of their importance in different areas of engineering, biomedical science, physics and mathematics
These techniques include the method of Homotopy analysis (HAM) [16, 26, 43], Variational literation (VIM) [15, 20, 24], Homotopy Perturbation (HPM)[8, 16, 20], Modified Decomposition (MDM) [34], Optimal Homotopy Asymptotic (OHAM) [13], Quintic B-spline (QBSM) [33], Non-Polynomial Spline (NPSM) [28], Eleven Degree Spline (EDSM) [29], Finite difference (FDM) [3], and Expfunction (EFM) [36 ] etc
For the study of 8th order boundary value problem (BVP) HPM was used by golbabai and javidi [8], differential quadrature method (DQM) by liu and wu[18],OHAM by haq et al [11], reproducing kernel space by Akram and Rehman [33, 2]
Summary
The researchers are targeting ordinary differentials equation because of their importance in different areas of engineering, biomedical science, physics and mathematics. Legendre wavelet owes some important properties such as good interpolation, less computational cost, better accuracy with a smaller number of collection points Motivated by these properties of the Legendre wavelet, we obtain approximate solutions of eight, tenth and twelfth order ordinary differential equation via LWCM in spectral mode was applied for the study of oscillatory type problems by Dizicheh.
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