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Sci. Comput."],"published-print":{"date-parts":[[2023,10,31]]},"abstract":"<jats:p>Abstract.<\/jats:p>\n                  <jats:p>In this paper we construct a quadrature scheme to numerically solve the nonlocal diffusion equation [Formula: see text] with [Formula: see text] the [Formula: see text]th power of the regularly accretive operator [Formula: see text]. Rigorous error analysis is carried out and sharp error bounds (up to some negligible constants) are obtained. The error estimates include a wide range of cases in which the regularity index and spectral angle of [Formula: see text], the smoothness of [Formula: see text], and the size of [Formula: see text] and [Formula: see text] are all involved. The quadrature scheme is exponentially convergent with respect to the step size and is root-exponentially convergent with respect to the number of solves. Some numerical tests are presented in the last section to verify the sharpness of our estimates. Furthermore, both the scheme and the error bounds can be utilized directly to solve and analyze time-dependent problems.<\/jats:p>","DOI":"10.1137\/22m1497298","type":"journal-article","created":{"date-parts":[[2023,9,21]],"date-time":"2023-09-21T16:48:00Z","timestamp":1695314880000},"page":"A2226-A2249","source":"Crossref","is-referenced-by-count":4,"title":["A Quadrature Scheme for Steady-State Diffusion Equations Involving Fractional Power of Regularly Accretive Operator"],"prefix":"10.1137","volume":"45","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9038-3644","authenticated-orcid":true,"given":"Beiping","family":"Duan","sequence":"first","affiliation":[{"name":"Faculty of Computational Mathematics and Cybernetics, Shenzhen MSU-BIT University, Shenzhen 518172, People\u2019s Republic of China."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2125-6932","authenticated-orcid":true,"given":"Zongze","family":"Yang","sequence":"additional","affiliation":[{"name":"Corresponding author. 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