{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,20]],"date-time":"2026-04-20T23:45:09Z","timestamp":1776728709984,"version":"3.51.2"},"reference-count":29,"publisher":"American Mathematical Society (AMS)","issue":"242","license":[{"start":{"date-parts":[[2003,3,8]],"date-time":"2003-03-08T00:00:00Z","timestamp":1047081600000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>\n                    A new highly accurate numerical approximation scheme based on a Gauss type Clenshaw-Curtis quadrature for Fredholm integral equations of the second kind\n                    <disp-formula content-type=\"math\/mathml\">\n                      \\[\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"x left-parenthesis t right-parenthesis plus integral Subscript a Superscript b Baseline k left-parenthesis t comma s right-parenthesis x left-parenthesis s right-parenthesis d s equals y left-parenthesis t right-parenthesis comma\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi>x<\/mml:mi>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:mi>t<\/mml:mi>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                            <mml:mo>+<\/mml:mo>\n                            <mml:msubsup>\n                              <mml:mo>\n                                \u222b\n                                \n                              <\/mml:mo>\n                              <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                                <mml:mi>a<\/mml:mi>\n                              <\/mml:mrow>\n                              <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                                <mml:mi>b<\/mml:mi>\n                              <\/mml:mrow>\n                            <\/mml:msubsup>\n                            <mml:mi>k<\/mml:mi>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:mi>t<\/mml:mi>\n                            <mml:mo>,<\/mml:mo>\n                            <mml:mi>s<\/mml:mi>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                            <mml:mi>x<\/mml:mi>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:mi>s<\/mml:mi>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                            <mml:mi>d<\/mml:mi>\n                            <mml:mi>s<\/mml:mi>\n                            <mml:mo>=<\/mml:mo>\n                            <mml:mi>y<\/mml:mi>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:mi>t<\/mml:mi>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                            <mml:mo>,<\/mml:mo>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">x(t)+\\int ^{b}_{a}k(t,s)x(s)ds=y(t),<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                      \\]\n                    <\/disp-formula>\n                    whose kernel\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"k left-parenthesis t comma s right-parenthesis\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi>k<\/mml:mi>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:mi>t<\/mml:mi>\n                            <mml:mo>,<\/mml:mo>\n                            <mml:mi>s<\/mml:mi>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">k(t,s)<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    is either discontinuous or not smooth along the main diagonal, is presented. This scheme is of spectral accuracy when\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"k left-parenthesis t comma s right-parenthesis\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi>k<\/mml:mi>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:mi>t<\/mml:mi>\n                            <mml:mo>,<\/mml:mo>\n                            <mml:mi>s<\/mml:mi>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">k(t,s)<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    is infinitely differentiable away from the diagonal\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"t equals s\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi>t<\/mml:mi>\n                            <mml:mo>=<\/mml:mo>\n                            <mml:mi>s<\/mml:mi>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">t = s<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    . Relation to the singular value decomposition is indicated. Application to integro-differential Schr\u00f6dinger equations with nonlocal potentials is given.\n                  <\/p>","DOI":"10.1090\/s0025-5718-02-01431-x","type":"journal-article","created":{"date-parts":[[2003,2,10]],"date-time":"2003-02-10T11:10:52Z","timestamp":1044875452000},"page":"729-756","source":"Crossref","is-referenced-by-count":25,"title":["Nystr\u00f6m-Clenshaw-Curtis quadrature for integral equations with discontinuous kernels"],"prefix":"10.1090","volume":"72","author":[{"given":"Sheon-Young","family":"Kang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Israel","family":"Koltracht","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"George","family":"Rawitscher","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"14","published-online":{"date-parts":[[2002,3,8]]},"reference":[{"key":"1","isbn-type":"print","volume-title":"Handbook of mathematical functions with formulas, graphs, and mathematical tables","year":"1992","ISBN":"https:\/\/id.crossref.org\/isbn\/0486612724"},{"issue":"5","key":"2","doi-asserted-by":"publisher","first-page":"1551","DOI":"10.1137\/S1064827597325141","article-title":"Hybrid Gauss-trapezoidal quadrature rules","volume":"20","author":"Alpert, Bradley K.","year":"1999","journal-title":"SIAM J. 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