In this work, Abel’s integral operator is represented based on Alpert’s multiwavelets as a sparse matrix and then a non-linear Abel’s integral equation of the second kind is solved by multiwavelets Galerkin method. Nonlinearity and singularity make the numerical procedure more challenging. But the proposed scheme overcomes these problems. Convergence analysis is investigated and some numerical examples validated this analysis.

中文翻译：

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Abel积分算子：基于多小波的稀疏表示

在这项工作中，基于Alpert的多小波将Abel积分算子表示为稀疏矩阵，然后通过多小波Galerkin方法求解第二类非线性Abel积分方程。非线性和奇异性使数值过程更具挑战性。但是提出的方案克服了这些问题。研究了收敛性分析，并通过一些数值例子验证了该分析。