Rational hybrid block method for solving Bratu-type boundary value problems
This study introduces a novel rational hybrid block method for solving Bratu-type boundary value problems, offering significant improvements in efficiency and accuracy. The method enhances the traditional block hybrid approach by incorporating rational approximations of grid points, which effectivel...
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| Format: | Article |
| Language: | English |
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Elsevier
2025-03-01
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| Series: | Partial Differential Equations in Applied Mathematics |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2666818125000191 |
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| author | S.S. Motsa S.D. Oloniiju H. Sithole-Mthethwa |
| author_facet | S.S. Motsa S.D. Oloniiju H. Sithole-Mthethwa |
| author_sort | S.S. Motsa |
| collection | DOAJ |
| description | This study introduces a novel rational hybrid block method for solving Bratu-type boundary value problems, offering significant improvements in efficiency and accuracy. The method enhances the traditional block hybrid approach by incorporating rational approximations of grid points, which effectively reduce local truncation errors and improve numerical stability. Unlike existing methods, the proposed technique provides higher precision with fewer computational resources, making it particularly advantageous for problems requiring fine resolution. Extensive numerical experimentation on selected Bratu-type problems demonstrates superior performance in terms of convergence and accuracy, especially when using carefully optimized parameters. Moreover, the method’s robustness and adaptability make it well-suited for handling challenging problems, such as those involving bifurcations or steep gradients. These advantages position the method as a powerful tool for solving complex boundary value problems with broad applications in engineering and the physical sciences. |
| format | Article |
| id | doaj-art-e6777bc14d7b402fa90cb91b8cae6aa3 |
| institution | Kabale University |
| issn | 2666-8181 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Partial Differential Equations in Applied Mathematics |
| spelling | doaj-art-e6777bc14d7b402fa90cb91b8cae6aa32025-01-30T05:15:07ZengElsevierPartial Differential Equations in Applied Mathematics2666-81812025-03-0113101091Rational hybrid block method for solving Bratu-type boundary value problemsS.S. Motsa0S.D. Oloniiju1H. Sithole-Mthethwa2Mathematics Department, University of Eswatini, Private Bag 4, Kwaluseni M201, Eswatini; School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Private Bag X01, Scottsville, Pietermaritzburg 3201, South AfricaDepartment of Mathematics, Rhodes University, Makhanda, PO Box 94, Grahamstown 6140, South Africa; Corresponding author.School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Private Bag X01, Scottsville, Pietermaritzburg 3201, South AfricaThis study introduces a novel rational hybrid block method for solving Bratu-type boundary value problems, offering significant improvements in efficiency and accuracy. The method enhances the traditional block hybrid approach by incorporating rational approximations of grid points, which effectively reduce local truncation errors and improve numerical stability. Unlike existing methods, the proposed technique provides higher precision with fewer computational resources, making it particularly advantageous for problems requiring fine resolution. Extensive numerical experimentation on selected Bratu-type problems demonstrates superior performance in terms of convergence and accuracy, especially when using carefully optimized parameters. Moreover, the method’s robustness and adaptability make it well-suited for handling challenging problems, such as those involving bifurcations or steep gradients. These advantages position the method as a powerful tool for solving complex boundary value problems with broad applications in engineering and the physical sciences.http://www.sciencedirect.com/science/article/pii/S2666818125000191Rational hybrid block methodRational approximationsError reductionBratu problem |
| spellingShingle | S.S. Motsa S.D. Oloniiju H. Sithole-Mthethwa Rational hybrid block method for solving Bratu-type boundary value problems Partial Differential Equations in Applied Mathematics Rational hybrid block method Rational approximations Error reduction Bratu problem |
| title | Rational hybrid block method for solving Bratu-type boundary value problems |
| title_full | Rational hybrid block method for solving Bratu-type boundary value problems |
| title_fullStr | Rational hybrid block method for solving Bratu-type boundary value problems |
| title_full_unstemmed | Rational hybrid block method for solving Bratu-type boundary value problems |
| title_short | Rational hybrid block method for solving Bratu-type boundary value problems |
| title_sort | rational hybrid block method for solving bratu type boundary value problems |
| topic | Rational hybrid block method Rational approximations Error reduction Bratu problem |
| url | http://www.sciencedirect.com/science/article/pii/S2666818125000191 |
| work_keys_str_mv | AT ssmotsa rationalhybridblockmethodforsolvingbratutypeboundaryvalueproblems AT sdoloniiju rationalhybridblockmethodforsolvingbratutypeboundaryvalueproblems AT hsitholemthethwa rationalhybridblockmethodforsolvingbratutypeboundaryvalueproblems |