{"id":"https://openalex.org/W1975143340","doi":"https://doi.org/10.1155/2014/654978","title":"Approximate Analytical Solutions for Mathematical Model of Tumour Invasion and Metastasis Using Modified Adomian Decomposition and Homotopy Perturbation Methods","display_name":"Approximate Analytical Solutions for Mathematical Model of Tumour Invasion and Metastasis Using Modified Adomian Decomposition and Homotopy Perturbation Methods","publication_year":2014,"publication_date":"2014-01-01","ids":{"openalex":"https://openalex.org/W1975143340","doi":"https://doi.org/10.1155/2014/654978","mag":"1975143340"},"language":"en","primary_location":{"id":"doi:10.1155/2014/654978","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2014/654978","pdf_url":"https://downloads.hindawi.com/journals/jam/2014/654978.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869","https://openalex.org/P4310320595"],"host_organization_lineage_names":["Hindawi Publishing Corporation","Wiley"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://downloads.hindawi.com/journals/jam/2014/654978.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5082377361","display_name":"Norhasimah Mahiddin","orcid":null},"institutions":[{"id":"https://openalex.org/I33849332","display_name":"University of Malaya","ror":"https://ror.org/00rzspn62","country_code":"MY","type":"education","lineage":["https://openalex.org/I33849332"]}],"countries":["MY"],"is_corresponding":true,"raw_author_name":"Norhasimah Mahiddin","raw_affiliation_strings":["Institute of Mathematical Sciences, University of Malaya, 50603 Kuala Lumpur, Malaysia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Mathematical Sciences, University of Malaya, 50603 Kuala Lumpur, Malaysia","institution_ids":["https://openalex.org/I33849332"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5103338685","display_name":"Siti Aishah Hashim Ali","orcid":null},"institutions":[{"id":"https://openalex.org/I72700828","display_name":"Open University Malaysia","ror":"https://ror.org/037yy5v69","country_code":"MY","type":"education","lineage":["https://openalex.org/I72700828"]}],"countries":["MY"],"is_corresponding":false,"raw_author_name":"S. A. Hashim Ali","raw_affiliation_strings":["Faculty of Science & Technology, Open University Malaysia, 50603 Kuala Lumpur, Malaysia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Science & Technology, Open University Malaysia, 50603 Kuala Lumpur, Malaysia","institution_ids":["https://openalex.org/I72700828"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5082377361"],"corresponding_institution_ids":["https://openalex.org/I33849332"],"apc_list":{"value":1130,"currency":"USD","value_usd":1130},"apc_paid":{"value":1130,"currency":"USD","value_usd":1130},"fwci":0.468,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.63039056,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"2014","issue":null,"first_page":"1","last_page":"13"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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/T11829","display_name":"Mathematical Biology Tumor Growth","score":0.9983999729156494,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9742000102996826,"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/adomian-decomposition-method","display_name":"Adomian decomposition method","score":0.9851371049880981},{"id":"https://openalex.org/keywords/linearization","display_name":"Linearization","score":0.8054303526878357},{"id":"https://openalex.org/keywords/homotopy-perturbation-method","display_name":"Homotopy perturbation method","score":0.7742243409156799},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.7436771988868713},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7206394076347351},{"id":"https://openalex.org/keywords/homotopy-analysis-method","display_name":"Homotopy analysis method","score":0.6904194355010986},{"id":"https://openalex.org/keywords/perturbation","display_name":"Perturbation (astronomy)","score":0.5841673612594604},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.5764609575271606},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5375743508338928},{"id":"https://openalex.org/keywords/decomposition","display_name":"Decomposition","score":0.5076175928115845},{"id":"https://openalex.org/keywords/homotopy","display_name":"Homotopy","score":0.4871320426464081},{"id":"https://openalex.org/keywords/decomposition-method","display_name":"Decomposition method (queueing theory)","score":0.44717147946357727},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.3988986611366272},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.39740708470344543},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.15963569283485413},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.15159600973129272},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.1023399829864502},{"id":"https://openalex.org/keywords/chemistry","display_name":"Chemistry","score":0.05995151400566101}],"concepts":[{"id":"https://openalex.org/C120317633","wikidata":"https://www.wikidata.org/wiki/Q3042796","display_name":"Adomian decomposition method","level":3,"score":0.9851371049880981},{"id":"https://openalex.org/C11210021","wikidata":"https://www.wikidata.org/wiki/Q1520713","display_name":"Linearization","level":3,"score":0.8054303526878357},{"id":"https://openalex.org/C91328119","wikidata":"https://www.wikidata.org/wiki/Q17030668","display_name":"Homotopy perturbation method","level":3,"score":0.7742243409156799},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.7436771988868713},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7206394076347351},{"id":"https://openalex.org/C173636693","wikidata":"https://www.wikidata.org/wiki/Q17030668","display_name":"Homotopy analysis method","level":3,"score":0.6904194355010986},{"id":"https://openalex.org/C177918212","wikidata":"https://www.wikidata.org/wiki/Q803623","display_name":"Perturbation (astronomy)","level":2,"score":0.5841673612594604},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5764609575271606},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5375743508338928},{"id":"https://openalex.org/C124681953","wikidata":"https://www.wikidata.org/wiki/Q339062","display_name":"Decomposition","level":2,"score":0.5076175928115845},{"id":"https://openalex.org/C5961521","wikidata":"https://www.wikidata.org/wiki/Q746083","display_name":"Homotopy","level":2,"score":0.4871320426464081},{"id":"https://openalex.org/C2778258933","wikidata":"https://www.wikidata.org/wiki/Q16918986","display_name":"Decomposition method (queueing theory)","level":2,"score":0.44717147946357727},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.3988986611366272},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.39740708470344543},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.15963569283485413},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.15159600973129272},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.1023399829864502},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.05995151400566101},{"id":"https://openalex.org/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","level":1,"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/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1155/2014/654978","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2014/654978","pdf_url":"https://downloads.hindawi.com/journals/jam/2014/654978.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869","https://openalex.org/P4310320595"],"host_organization_lineage_names":["Hindawi Publishing Corporation","Wiley"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:eprints.oum.edu.my:935","is_oa":false,"landing_page_url":"http://www.hindawi.com/journals/jam/2014/654978/cta/","pdf_url":null,"source":{"id":"https://openalex.org/S4306400156","display_name":"Knowledge based platform (Open University Malaysia)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I72700828","host_organization_name":"Open University Malaysia","host_organization_lineage":["https://openalex.org/I72700828"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":null,"raw_type":"Article"},{"id":"pmh:oai:CULeuclid:euclid.jam/1395855298","is_oa":false,"landing_page_url":"https://projecteuclid.org/euclid.jam/1395855298","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},{"id":"pmh:oai:RePEc:hin:jnljam:654978","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/JAM/2014/654978.xml","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},{"id":"pmh:oai:doaj.org/article:90988b62de624218b72cd8f7880d27fc","is_oa":true,"landing_page_url":"https://doaj.org/article/90988b62de624218b72cd8f7880d27fc","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of Applied Mathematics, Vol 2014 (2014)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2014/654978","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2014/654978","pdf_url":"https://downloads.hindawi.com/journals/jam/2014/654978.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869","https://openalex.org/P4310320595"],"host_organization_lineage_names":["Hindawi Publishing Corporation","Wiley"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G7426611736","display_name":null,"funder_award_id":"P0257/2007A","funder_id":"https://openalex.org/F4320322604","funder_display_name":"Universiti Malaya"}],"funders":[{"id":"https://openalex.org/F4320322604","display_name":"Universiti Malaya","ror":"https://ror.org/00rzspn62"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1975143340.pdf","grobid_xml":"https://content.openalex.org/works/W1975143340.grobid-xml"},"referenced_works_count":14,"referenced_works":["https://openalex.org/W1914839904","https://openalex.org/W1964615735","https://openalex.org/W1995602881","https://openalex.org/W1998123047","https://openalex.org/W2015496903","https://openalex.org/W2018381864","https://openalex.org/W2032632404","https://openalex.org/W2048195900","https://openalex.org/W2052665734","https://openalex.org/W2088254252","https://openalex.org/W2112099906","https://openalex.org/W2141673032","https://openalex.org/W2163778004","https://openalex.org/W2165917005"],"related_works":["https://openalex.org/W2088184017","https://openalex.org/W2027675706","https://openalex.org/W2316939131","https://openalex.org/W2143027225","https://openalex.org/W2139354281","https://openalex.org/W2376649588","https://openalex.org/W2264375321","https://openalex.org/W2024752839","https://openalex.org/W2027467829","https://openalex.org/W2079425938"],"abstract_inverted_index":{"The":[0,26,45,82],"modified":[1],"decomposition":[2,63],"method":[3,8,64],"(MDM)":[4],"and":[5,24,36,51,61],"homotopy":[6],"perturbation":[7],"(HPM)":[9],"are":[10],"applied":[11],"to":[12,39],"obtain":[13],"the":[14,18,29,33,56,71,74,91,103],"approximate":[15,83],"solution":[16,85,92],"of":[17,21,32,73],"nonlinear":[19,41,109],"model":[20],"tumour":[22],"invasion":[23],"metastasis.":[25],"study":[27],"highlights":[28],"significant":[30],"features":[31],"employed":[34],"methods":[35,46],"their":[37],"ability":[38],"handle":[40],"partial":[42],"differential":[43],"equations.":[44],"do":[47],"not":[48,101],"need":[49],"linearization":[50],"weak":[52],"nonlinearity":[53],"assumptions.":[54],"Although":[55],"main":[57],"difference":[58],"between":[59],"MDM":[60,88],"Adomian":[62,104],"(ADM)":[65],"is":[66],"a":[67],"slight":[68],"variation":[69],"in":[70],"definition":[72],"initial":[75],"condition,":[76],"modification":[77],"eliminates":[78],"massive":[79],"computation":[80],"work.":[81],"analytical":[84],"obtained":[86,93],"by":[87,94],"logically":[89],"contains":[90],"HPM.":[95],"It":[96],"shows":[97],"that":[98],"HPM":[99],"does":[100],"involve":[102],"polynomials":[105],"when":[106],"dealing":[107],"with":[108],"problems.":[110]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2026-08-21T09:56:20.448147","created_date":"2025-10-10T00:00:00"}
