{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,5]],"date-time":"2022-04-05T03:44:52Z","timestamp":1649130292101},"reference-count":25,"publisher":"Hindawi Limited","license":[{"start":{"date-parts":[[2012,12,5]],"date-time":"2012-12-05T00:00:00Z","timestamp":1354665600000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"name":"Department of Science and Technology, New Delhi"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Advances in Numerical Analysis"],"published-print":{"date-parts":[[2012,12,5]]},"abstract":"<jats:p>We present a fourth order finite difference method for doubly singular boundary value problem <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\"><mml:mrow><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mi>p<\/mml:mi><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mi>x<\/mml:mi><mml:mo stretchy=\"false\">)<\/mml:mo><mml:mrow><mml:mi>y<\/mml:mi><\/mml:mrow><mml:mrow><mml:mi>\u2032<\/mml:mi><\/mml:mrow><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mi>x<\/mml:mi><mml:mo stretchy=\"false\">)<\/mml:mo><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:mrow><mml:mi>\u2032<\/mml:mi><mml:mo>=<\/mml:mo><mml:mi>q<\/mml:mi><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mi>x<\/mml:mi><mml:mo stretchy=\"false\">)<\/mml:mo><mml:mi>f<\/mml:mi><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mi>x<\/mml:mi><mml:mo>,<\/mml:mo><mml:mi>y<\/mml:mi><mml:mo stretchy=\"false\">)<\/mml:mo><mml:mo>,<\/mml:mo><mml:mi>\u2009\u2009<\/mml:mi><mml:mn>0<\/mml:mn><mml:mo>&lt;<\/mml:mo><mml:mi>x<\/mml:mi><mml:mi>\u2009\u2009<\/mml:mi><mml:mo>\u2264<\/mml:mo><mml:mn>1<\/mml:mn><\/mml:math> with boundary conditions <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M2\"><mml:mi>y<\/mml:mi><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mn>0<\/mml:mn><mml:mo stretchy=\"false\">)<\/mml:mo><mml:mo>=<\/mml:mo><mml:mi>A<\/mml:mi><mml:mi>\u2009<\/mml:mi><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mtext>or<\/mml:mtext><mml:mi>\u2009\u2009<\/mml:mi><mml:mi>y<\/mml:mi><mml:mi>'<\/mml:mi><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mn>0<\/mml:mn><mml:mo stretchy=\"false\">)<\/mml:mo><mml:mo>=<\/mml:mo><mml:mn>0<\/mml:mn><mml:mi>\u2009\u2009<\/mml:mi><mml:mtext>or<\/mml:mtext><mml:mi>\u2009\u2009<\/mml:mi><mml:msub><mml:mrow><mml:mi>lim<\/mml:mi><\/mml:mrow><mml:mrow><mml:mi>x<\/mml:mi><mml:mo>\u2192<\/mml:mo><mml:mn>0<\/mml:mn><\/mml:mrow><\/mml:msub><mml:mi>p<\/mml:mi><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mi>x<\/mml:mi><mml:mo stretchy=\"false\">)<\/mml:mo><mml:mi>y<\/mml:mi><mml:mi>'<\/mml:mi><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mi>x<\/mml:mi><mml:mo stretchy=\"false\">)<\/mml:mo><mml:mo>=<\/mml:mo><mml:mn>0<\/mml:mn><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:math> and <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M3\"><mml:mi>\u03b1<\/mml:mi><mml:mi>y<\/mml:mi><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mn>1<\/mml:mn><mml:mo stretchy=\"false\">)<\/mml:mo><mml:mo>+<\/mml:mo><mml:mi>\u2009<\/mml:mi><mml:mi>\u03b2<\/mml:mi><mml:mi>y<\/mml:mi><mml:mi>'<\/mml:mi><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mn>1<\/mml:mn><mml:mo stretchy=\"false\">)<\/mml:mo><mml:mo>=<\/mml:mo><mml:mi>\u03b3<\/mml:mi><\/mml:math>, where <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M4\"><mml:mi>\u03b1<\/mml:mi><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mo>&gt;<\/mml:mo><mml:mn>0<\/mml:mn><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:math>, <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M5\"><mml:mi>\u2009<\/mml:mi><mml:mi>\u03b2<\/mml:mi><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mo>\u2265<\/mml:mo><mml:mn>0<\/mml:mn><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:math>, <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M6\"><mml:mi>\u2009<\/mml:mi><mml:mi>\u03b3<\/mml:mi><\/mml:math> and <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M7\"><mml:mrow><mml:mi>A<\/mml:mi><\/mml:mrow><\/mml:math> are finite constants. Here <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M8\"><mml:mi>p<\/mml:mi><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mn>0<\/mml:mn><mml:mo stretchy=\"false\">)<\/mml:mo><mml:mo>=<\/mml:mo><mml:mn>0<\/mml:mn><\/mml:math> and <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M9\"><mml:mi>q<\/mml:mi><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mi>x<\/mml:mi><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:math> is allowed to be discontinuous at the singular point <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M10\"><mml:mi>x<\/mml:mi><mml:mo>=<\/mml:mo><mml:mn>0<\/mml:mn><\/mml:math>. The method is based on uniform mesh. The accuracy of the method is established under quite general conditions and also corroborated through one numerical example.<\/jats:p>","DOI":"10.1155\/2012\/349618","type":"journal-article","created":{"date-parts":[[2012,12,5]],"date-time":"2012-12-05T23:54:56Z","timestamp":1354751696000},"page":"1-21","source":"Crossref","is-referenced-by-count":3,"title":["A Note on Fourth Order Method for Doubly Singular Boundary Value Problems"],"prefix":"10.1155","volume":"2012","author":[{"given":"R. K.","family":"Pandey","sequence":"first","affiliation":[{"name":"Department of Mathematics, Indian Institute of Technology, Kharagpur 721302, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"G. 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