A wavelet Petrov-Galerkin method for solving integro-differential equations. (English) Zbl 1170.65337

Summary: We solve integro-differential equation by using the Alpert multiwavelets as basis functions. We also use the orthogonality of the basis of the trial and test spaces in the Petrov-Galerkin method. The computations are reduced because of orthogonality. Thus the final system that we get from discretizing the integro-differential equation has a very small dimension and enough accuracy. We compare the results with [M. Lakestani, M. Razzaghi and M. Dehghan, Math. Probl. Eng. 2006 (2006)] and [A. Ayad, Stud. Univ. Babeş-Bolyai, Math. 41, No. 3, 1–8 (1996; Zbl 1009.65082)] which used a system of much larger dimension and got less accurate results. In [Z. Chen and Y. Xu, SIAM J. Numer. Anal. 35, No. 1, 406–434 (1998; Zbl 0911.65143)], convergence of Petrov-Galerkin method has been discussed with some restrictions on degrees of chosen polynomial basis, but in this paper convergence is obtained for every degree.


65R20 Numerical methods for integral equations
Full Text: DOI


[1] DOI: 10.1137/0524016 · Zbl 0764.42017
[2] DOI: 10.1017/CBO9780511626340
[3] Ayad A., Studia Univ. Babes-Bolyai, Math 41 pp 1– (1996)
[4] DOI: 10.1137/S0036142996297217 · Zbl 0911.65143
[5] Kreyszing E., Introductory Functional Analysis with Applications (1978)
[6] DOI: 10.1155/MPE/2006/96184 · Zbl 1200.65112
[7] DOI: 10.1016/j.amc.2004.04.109 · Zbl 1073.65148
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.