{"id":"https://openalex.org/W2279204806","doi":"https://doi.org/10.1142/s1793962316500069","title":"An exponential expanding meshes sequence and finite difference method adopted for two-dimensional elliptic equations","display_name":"An exponential expanding meshes sequence and finite difference method adopted for two-dimensional elliptic equations","publication_year":2015,"publication_date":"2015-12-23","ids":{"openalex":"https://openalex.org/W2279204806","doi":"https://doi.org/10.1142/s1793962316500069","mag":"2279204806"},"language":"en","primary_location":{"id":"doi:10.1142/s1793962316500069","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793962316500069","pdf_url":null,"source":{"id":"https://openalex.org/S107361000","display_name":"Advances in Complex Systems","issn_l":"0219-5259","issn":["0219-5259","1793-6802","1793-9615","1793-9623"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Modeling, Simulation, and Scientific Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5036252741","display_name":"Navnit Jha","orcid":"https://orcid.org/0000-0001-7884-8640"},"institutions":[{"id":"https://openalex.org/I90425906","display_name":"South Asian University","ror":"https://ror.org/02kjyst95","country_code":"IN","type":"education","lineage":["https://openalex.org/I90425906"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Navnit Jha","raw_affiliation_strings":["Faculty of Mathematics and Computer Science, Department of Mathematics, South Asian University, Chanakyapuri, New Delhi 110 021, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Mathematics and Computer Science, Department of Mathematics, South Asian University, Chanakyapuri, New Delhi 110 021, India","institution_ids":["https://openalex.org/I90425906"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5084231289","display_name":"Neelesh Kumar","orcid":"https://orcid.org/0000-0003-1384-8652"},"institutions":[{"id":"https://openalex.org/I90425906","display_name":"South Asian University","ror":"https://ror.org/02kjyst95","country_code":"IN","type":"education","lineage":["https://openalex.org/I90425906"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Neelesh Kumar","raw_affiliation_strings":["Faculty of Mathematics and Computer Science, Department of Mathematics, South Asian University, Chanakyapuri, New Delhi 110 021, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Mathematics and Computer Science, Department of Mathematics, South Asian University, Chanakyapuri, New Delhi 110 021, India","institution_ids":["https://openalex.org/I90425906"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I90425906"],"apc_list":null,"apc_paid":null,"fwci":0.9826,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.76898353,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"07","issue":"02","first_page":"1650006","last_page":"1650006"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6770439743995667},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.61992347240448},{"id":"https://openalex.org/keywords/finite-difference","display_name":"Finite difference","score":0.6143302917480469},{"id":"https://openalex.org/keywords/finite-difference-method","display_name":"Finite difference method","score":0.5908041000366211},{"id":"https://openalex.org/keywords/polygon-mesh","display_name":"Polygon mesh","score":0.5744943022727966},{"id":"https://openalex.org/keywords/elliptic-partial-differential-equation","display_name":"Elliptic partial differential equation","score":0.5655860304832458},{"id":"https://openalex.org/keywords/truncation-error","display_name":"Truncation error","score":0.5306960940361023},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5100017786026001},{"id":"https://openalex.org/keywords/elliptic-curve","display_name":"Elliptic curve","score":0.49012503027915955},{"id":"https://openalex.org/keywords/finite-volume-method-for-one-dimensional-steady-state-diffusion","display_name":"Finite volume method for one-dimensional steady state diffusion","score":0.4660326838493347},{"id":"https://openalex.org/keywords/matrix-exponential","display_name":"Matrix exponential","score":0.45128920674324036},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.45085424184799194},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4354993999004364},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.43195247650146484},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.42238226532936096},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.3817155361175537},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.13479167222976685},{"id":"https://openalex.org/keywords/numerical-partial-differential-equations","display_name":"Numerical partial differential equations","score":0.11745068430900574}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6770439743995667},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.61992347240448},{"id":"https://openalex.org/C181330731","wikidata":"https://www.wikidata.org/wiki/Q2068418","display_name":"Finite difference","level":2,"score":0.6143302917480469},{"id":"https://openalex.org/C205951836","wikidata":"https://www.wikidata.org/wiki/Q1147751","display_name":"Finite difference method","level":2,"score":0.5908041000366211},{"id":"https://openalex.org/C31487907","wikidata":"https://www.wikidata.org/wiki/Q1154597","display_name":"Polygon mesh","level":2,"score":0.5744943022727966},{"id":"https://openalex.org/C54067925","wikidata":"https://www.wikidata.org/wiki/Q3607962","display_name":"Elliptic partial differential equation","level":3,"score":0.5655860304832458},{"id":"https://openalex.org/C104942944","wikidata":"https://www.wikidata.org/wiki/Q3434686","display_name":"Truncation error","level":2,"score":0.5306960940361023},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5100017786026001},{"id":"https://openalex.org/C179603306","wikidata":"https://www.wikidata.org/wiki/Q268493","display_name":"Elliptic curve","level":2,"score":0.49012503027915955},{"id":"https://openalex.org/C85405225","wikidata":"https://www.wikidata.org/wiki/Q17013617","display_name":"Finite volume method for one-dimensional steady state diffusion","level":4,"score":0.4660326838493347},{"id":"https://openalex.org/C195906000","wikidata":"https://www.wikidata.org/wiki/Q1191722","display_name":"Matrix exponential","level":3,"score":0.45128920674324036},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.45085424184799194},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4354993999004364},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.43195247650146484},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.42238226532936096},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.3817155361175537},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.13479167222976685},{"id":"https://openalex.org/C97826883","wikidata":"https://www.wikidata.org/wiki/Q7069659","display_name":"Numerical partial differential equations","level":3,"score":0.11745068430900574},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s1793962316500069","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793962316500069","pdf_url":null,"source":{"id":"https://openalex.org/S107361000","display_name":"Advances in Complex Systems","issn_l":"0219-5259","issn":["0219-5259","1793-6802","1793-9615","1793-9623"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Modeling, Simulation, and Scientific Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.8600000143051147,"id":"https://metadata.un.org/sdg/14","display_name":"Life below water"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":31,"referenced_works":["https://openalex.org/W577555718","https://openalex.org/W1481802162","https://openalex.org/W1590879322","https://openalex.org/W1652079258","https://openalex.org/W1974167413","https://openalex.org/W1975893845","https://openalex.org/W1976217016","https://openalex.org/W1987816244","https://openalex.org/W1997001904","https://openalex.org/W1999989603","https://openalex.org/W2015028305","https://openalex.org/W2017552483","https://openalex.org/W2019108007","https://openalex.org/W2028753024","https://openalex.org/W2033516351","https://openalex.org/W2042015995","https://openalex.org/W2061107295","https://openalex.org/W2067713762","https://openalex.org/W2076086347","https://openalex.org/W2077221255","https://openalex.org/W2102440316","https://openalex.org/W2102514286","https://openalex.org/W2102995950","https://openalex.org/W2152670102","https://openalex.org/W2163620187","https://openalex.org/W2795744704","https://openalex.org/W3035235874","https://openalex.org/W3142078155","https://openalex.org/W4242418012","https://openalex.org/W4299343067","https://openalex.org/W4299835338"],"related_works":["https://openalex.org/W3211167481","https://openalex.org/W1990789772","https://openalex.org/W2023230962","https://openalex.org/W3177726327","https://openalex.org/W3141047049","https://openalex.org/W3211186365","https://openalex.org/W2061368437","https://openalex.org/W2131466914","https://openalex.org/W1969161031","https://openalex.org/W2279204806"],"abstract_inverted_index":{"We":[0],"demonstrate":[1],"a":[2,34,59,64,73,84,148],"new":[3],"nonuniform":[4],"mesh":[5,92],"finite":[6,52],"difference":[7,131],"method":[8,29],"to":[9,136],"obtain":[10],"accurate":[11],"solutions":[12],"for":[13],"the":[14,42,49,78,99,106,112,120,127,156,162],"elliptic":[15,150],"partial":[16,25],"differential":[17],"equations":[18],"in":[19,47,77],"two":[20],"dimensions":[21],"with":[22,98,119],"nonlinear":[23],"first-order":[24],"derivative":[26],"terms.":[27],"The":[28,87,103,130,152],"will":[30,81],"be":[31],"based":[32],"on":[33],"geometric":[35,91],"grid":[36],"network":[37],"area":[38],"and":[39,72,115,147,159],"included":[40],"among":[41],"most":[43],"stable":[44],"differencing":[45],"scheme":[46,107,132],"which":[48],"nine-point":[50],"spatial":[51],"differences":[53],"are":[54],"implemented,":[55],"thus":[56],"arriving":[57],"at":[58],"compact":[60],"formulation.":[61],"In":[62],"general,":[63],"third":[65],"order":[66,158],"of":[67,89,101,105,122,126,161],"accuracy":[68,160],"has":[69,95,108,133],"been":[70,96,109,134],"achieved":[71],"fourth-order":[74],"truncation":[75],"error":[76],"solution":[79],"values":[80],"follow":[82],"as":[83],"particular":[85],"case.":[86],"efficiency":[88],"using":[90,111],"ratio":[93],"parameter":[94],"shown":[97],"help":[100,121],"illustrations.":[102],"convergence":[104],"established":[110],"matrix":[113],"analysis,":[114],"irreducibility":[116],"is":[117],"proved":[118],"strongly":[123],"connected":[124],"characteristics":[125],"iteration":[128],"matrix.":[129],"applied":[135],"test":[137],"convection":[138],"diffusion":[139],"equation,":[140,144],"steady":[141],"state":[142],"Burger\u2019s":[143],"ocean":[145],"model":[146],"semi-linear":[149],"equation.":[151],"computational":[153],"results":[154],"confirm":[155],"theoretical":[157],"method.":[163]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}