{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T03:17:02Z","timestamp":1776827822122,"version":"3.51.2"},"reference-count":27,"publisher":"American Mathematical Society (AMS)","issue":"222","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>\n                    In this paper fitted finite difference methods on a uniform mesh with internodal spacing\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"h\">\n                        <mml:semantics>\n                          <mml:mi>h<\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">h<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    , are considered for a singularly perturbed semilinear two-point boundary value problem. It is proved that a scheme of this type with a frozen fitting factor cannot converge\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"epsilon\">\n                        <mml:semantics>\n                          <mml:mi>\n                            \u03b5\n                            \n                          <\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">\\varepsilon<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    -uniformly in the maximum norm to the solution of the differential equation as the mesh spacing\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"h\">\n                        <mml:semantics>\n                          <mml:mi>h<\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">h<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    goes to zero. Numerical experiments are presented which show that the same result is true for a number of schemes with variable fitting factors.\n                  <\/p>","DOI":"10.1090\/s0025-5718-98-00922-3","type":"journal-article","created":{"date-parts":[[2002,7,26]],"date-time":"2002-07-26T18:14:44Z","timestamp":1027707284000},"page":"603-617","source":"Crossref","is-referenced-by-count":23,"title":["On the non-existence of \ud835\udf00-uniform finite difference methods on uniform meshes for semilinear two-point boundary value problems"],"prefix":"10.1090","volume":"67","author":[{"given":"Paul","family":"Farrell","sequence":"first","affiliation":[]},{"given":"John","family":"Miller","sequence":"additional","affiliation":[]},{"given":"Eugene","family":"O\u2019Riordan","sequence":"additional","affiliation":[]},{"given":"Grigorii","family":"Shishkin","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[1998]]},"reference":[{"issue":"1","key":"1","doi-asserted-by":"publisher","first-page":"128","DOI":"10.1016\/0021-9991(91)90076-W","article-title":"Inadequacy of first-order upwind difference schemes for some recirculating flows","volume":"93","author":"Brandt, A.","year":"1991","journal-title":"J. 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