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Multi-Wavelets Galerkin Method for Solving the System of Volterra Integral Equations

Authors: 

Hoang Viet Long, Haifa Bin Jebreen*, Stefania Tomasiello

Source title: 
Mathematics, 8(8): 1369, 2020 (ISI)
Academic year of acceptance: 
2020-2021
Abstract: 

In this work, an efficient algorithm is proposed for solving the system of Volterra integral equations based on wavelet Galerkin method. This problem is reduced to a set of algebraic equations using the operational matrix of integration and wavelet transform matrix. For linear type, the computational effort decreases by thresholding. The convergence analysis of the proposed scheme has been investigated and it is shown that its convergence is of order O(2−Jr), where J is the refinement level and r is the multiplicity of multi-wavelets. Several numerical tests are provided to illustrate the ability and efficiency of the method.