{"doi":"10.1155/2022/9367638","title":"[Retracted] A Comparison of Finite Difference and Finite Volume Methods with Numerical Simulations: Burgers Equation Model","abstract":"<jats:p>In this paper, we present an intensive investigation of the finite volume method (FVM) compared to the finite difference methods (FDMs). In order to show the main difference in the way of approaching the solution, we take the Burgers equation and the Buckley–Leverett equation as examples to simulate the previously mentioned methods. On the one hand, we simulate the results of the finite difference methods using the schemes of Lax–Friedrichs and Lax–Wendroff. On the other hand, we apply Godunov’s scheme to simulate the results of the finite volume method. Moreover, we show how starting with a variational formulation of the problem, the finite element technique provides piecewise formulations of functions defined by a collection of grid data points, while the finite difference technique begins with a differential formulation of the problem and continues to discretize the derivatives. Finally, some graphical and numerical comparisons are provided to illustrate and corroborate the differences between these two main methods.</jats:p>","journal":"Complexity","year":2022,"id":23260,"datarank":2.1971956943598947,"base_score":3.8918202981106265,"endowment":3.8918202981106265,"self_citation_contribution":0.5837730447165941,"citation_network_contribution":1.6134226496433004,"self_endowment_contribution":0.5837730447165941,"citer_contribution":1.6134226496433004,"corpus_percentile":null,"corpus_rank":null,"citation_count":48,"citer_count":37,"citers_with_citation_signal":23,"citers_with_endowment":23,"datacite_reuse_total":0,"is_dataset":false,"is_dataset_confidence":null,"is_data_producer":false,"deposit_databanks":null,"is_oa":false,"file_count":0,"downloads":0,"has_version_chain":false,"published_date":null,"fair_score":null,"fair_percentile":null,"algorithm_id":"datarank_citation_only_1hop_v6","ranking_scope":"data_only","authors":[{"id":143425,"name":"Ahmed Shawki Jaber","orcid":null,"position":1,"is_corresponding":false},{"id":143426,"name":"Mustafa T. Yaseen","orcid":null,"position":2,"is_corresponding":false},{"id":143427,"name":"Mohammed Rasheed","orcid":null,"position":3,"is_corresponding":false},{"id":143428,"name":"Omer Bazighifan","orcid":"0000-0002-7251-9608","position":4,"is_corresponding":false},{"id":143429,"name":"Taher A. Nofal","orcid":null,"position":5,"is_corresponding":false},{"id":143424,"name":"Ali Hasan Ali","orcid":"0000-0003-2959-4212","position":0,"is_corresponding":false}],"reference_count":0,"raw_metadata":{"has_enrichment":true,"base_score":3.8918202981106265,"endowment":3.8918202981106265,"datacite_reuse_total":0,"file_count":0,"downloads":0,"views":0,"has_version_chain":false,"is_dataset":false,"is_oa":false,"pmid":"21071399","pmcid":null,"openalex_id":"https://openalex.org/W4283652870","authors":[],"funders":[{"funder_name":"Taif University","grant_id":"TURSP-2020/031","title":null}],"total_grants":1,"fwci":7.634,"citation_percentile":0.9883174,"influential_citations":0,"citation_trend":[{"year":2022,"count":4},{"year":2023,"count":23},{"year":2024,"count":7},{"year":2025,"count":12},{"year":2026,"count":2}],"oa_status":"gold","license":"cc-by","oa_locations":[{"url":"https://downloads.hindawi.com/journals/complexity/2022/9367638.pdf","host_type":"journal"},{"url":"https://downloads.hindawi.com/journals/complexity/2022/9367638.pdf","host_type":"GOLD"},{"url":"https://downloads.hindawi.com/journals/complexity/2022/9367638.pdf","host_type":"publisher"},{"url":"https://onlinelibrary.wiley.com/doi/pdf/10.1155/2022/9367638","host_type":"publisher"},{"url":"https://onlinelibrary.wiley.com/doi/full-xml/10.1155/2022/9367638","host_type":"publisher"},{"url":"https://doi.org/10.1155/2022/9367638","host_type":"journal"},{"url":"http://downloads.hindawi.com/journals/complexity/2022/9367638.xml","host_type":"repository"},{"url":"https://doaj.org/article/6f4903f06f0e4f0ea5c30b71170cbc5c","host_type":"repository"}],"fields_of_study":["Advanced Numerical Methods in Computational Mathematics","Computational Fluid Dynamics and Aerodynamics","Numerical methods in engineering","Computer Science","Physics","Mathematics"],"mesh_terms":[],"keywords":["Finite volume method","Mathematics","Finite difference method","Finite difference","Finite volume method for one-dimensional steady state diffusion","Finite element method","Burgers' equation","Discretization","Finite difference coefficient","Piecewise","Applied mathematics","Partial differential equation","Regular grid","Mathematical analysis","Mixed finite element method","Grid","Geometry","Numerical partial differential equations","Mechanics","Physics"],"sdg_mappings":[],"linked_datasets":[],"clinical_trials":[],"software_tools":[],"database_accessions":[],"source":"live","citation_network_status":"fetched"},"created_at":"2026-06-07T18:53:31.174302Z","pmid":null,"pmcid":null,"fwci":null,"citation_percentile":null,"influential_citations":0,"oa_status":null,"license":null,"views":0,"total_file_size_bytes":0,"version_count":0,"fair_f":null,"fair_a":null,"fair_i":null,"fair_r":null,"fair_zscore":null,"fair_rationale":null,"fair_model":null,"fair_agent_version":null,"fair_fulltext_source":null,"fair_has_llm":null,"fair_computed_at":null,"clinical_trials":[],"software_tools":[],"db_accessions":[],"linked_datasets":[],"topics":[]}