In this study, an approximation method with an integral operational matrix based on the Muntz wavelets basis is presented to solve the variational problems of moving or fixed boundary conditions and a computational algorithm is given for the suggested approach. First, the integral operational matrix is created through the Muntz wavelets. Then, by using this integral operational matrix with Lagrange multipliers, the present approach reduces the variational problem into the system of algebraic equations. This approach is examined by some illustrative examples, and the acquired results prove that the suggested approach can solve the variational problems effectively with higher accuracy. The proposed approach yields better and comparable results with some other existing schemes given in the literature. The approximate wavelet solutions derived by the suggested approach are very identical to the corresponding exact solution.

在这项研究中，提出了一种基于Muntz小波的具有积分运算矩阵的近似方法，以解决移动或固定边界条件的变分问题，并为该方法给出了一种计算算法。首先，通过Muntz小波创建积分运算矩阵。然后，通过将该积分运算矩阵与拉格朗日乘子一起使用，本方法将变分问题简化为代数方程组。通过一些实例验证了该方法的有效性，所获得的结果证明了所提出的方法能够以较高的精度有效地解决变分问题。与文献中给出的其他一些现有方案相比，所提出的方法产生了更好的可比结果。