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Some differences exist in (21) because of the shape functions that are used in the MWGM. First, (21) has [0, L] as integral domains.
Figure 1 shows the relatively simple Hat wavelet functions, which are constructed with (9) and (11) and are used as the basis functions of the MWGM. Usually, (9) is called basic scaling functions and (11) is called wavelet functions.
The integer k will be finite to be used in the weak form of the MWGM because the infinity of k cannot be used in the numerical analysis.
The aim of this study was to formulate a Meshless Wavelet Galerkin Method (MWGM) to solve a pair of 2nd-order elliptic differential equations, in other words, the Timoshenko beam differential equation using Hat wavelets.
With the above considerations, the following properties should be satisfied to use these functions as basic functions for MWGM.
This paper examined and discussed the MWGM formulation for a first-order shear deformable beam, the properties of the MWGM, the differences between the MWGM and EFG, and programming methods for the MWGM.
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