A Matrix Spline Method for a Class of Fourth-Order Ordinary Differential Problems
Differential matrix models provide an elementary blueprint for the adequate and efficient treatment of many important applications in science and engineering. In the present work, we suggest a procedure, extending our previous research results, to represent the solutions of nonlinear matrix differen...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-08-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/16/2826 |
| _version_ | 1797443722158276608 |
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| author | Michael M. Tung Emilio Defez Javier Ibáñez José M. Alonso Julia Real-Herráiz |
| author_facet | Michael M. Tung Emilio Defez Javier Ibáñez José M. Alonso Julia Real-Herráiz |
| author_sort | Michael M. Tung |
| collection | DOAJ |
| description | Differential matrix models provide an elementary blueprint for the adequate and efficient treatment of many important applications in science and engineering. In the present work, we suggest a procedure, extending our previous research results, to represent the solutions of nonlinear matrix differential problems of fourth order given in the form <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mi>Y</mi><mrow><mo>(</mo><mn>4</mn><mo>)</mo></mrow></msup><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>=</mo><mi>f</mi><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mi>Y</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>)</mo></mrow></mrow></semantics></math></inline-formula> in terms of higher-order matrix splines. The corresponding algorithm is explained, and some numerical examples for the illustration of the method are included. |
| first_indexed | 2024-03-09T13:01:10Z |
| format | Article |
| id | doaj.art-cd9504f374554c77849c244fcda95e97 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T13:01:10Z |
| publishDate | 2022-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-cd9504f374554c77849c244fcda95e972023-11-30T21:54:15ZengMDPI AGMathematics2227-73902022-08-011016282610.3390/math10162826A Matrix Spline Method for a Class of Fourth-Order Ordinary Differential ProblemsMichael M. Tung0Emilio Defez1Javier Ibáñez2José M. Alonso3Julia Real-Herráiz4Instituto de Matemática Multidisciplinar, Universitat Politècnica de València, Camino de Vera s/n, 46022 Valencia, SpainInstituto de Matemática Multidisciplinar, Universitat Politècnica de València, Camino de Vera s/n, 46022 Valencia, SpainInstituto de Matemática Multidisciplinar, Universitat Politècnica de València, Camino de Vera s/n, 46022 Valencia, SpainInstituto de Instrumentación Para Imagen Molecular, Universitat Politècnica de València, Camino de Vera s/n, 46022 Valencia, SpainInstituto de Matemática Multidisciplinar, Universitat Politècnica de València, Camino de Vera s/n, 46022 Valencia, SpainDifferential matrix models provide an elementary blueprint for the adequate and efficient treatment of many important applications in science and engineering. In the present work, we suggest a procedure, extending our previous research results, to represent the solutions of nonlinear matrix differential problems of fourth order given in the form <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mi>Y</mi><mrow><mo>(</mo><mn>4</mn><mo>)</mo></mrow></msup><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>=</mo><mi>f</mi><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mi>Y</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>)</mo></mrow></mrow></semantics></math></inline-formula> in terms of higher-order matrix splines. The corresponding algorithm is explained, and some numerical examples for the illustration of the method are included.https://www.mdpi.com/2227-7390/10/16/2826matrix differential equationshigher-order matrix splinesnumerical algorithms |
| spellingShingle | Michael M. Tung Emilio Defez Javier Ibáñez José M. Alonso Julia Real-Herráiz A Matrix Spline Method for a Class of Fourth-Order Ordinary Differential Problems Mathematics matrix differential equations higher-order matrix splines numerical algorithms |
| title | A Matrix Spline Method for a Class of Fourth-Order Ordinary Differential Problems |
| title_full | A Matrix Spline Method for a Class of Fourth-Order Ordinary Differential Problems |
| title_fullStr | A Matrix Spline Method for a Class of Fourth-Order Ordinary Differential Problems |
| title_full_unstemmed | A Matrix Spline Method for a Class of Fourth-Order Ordinary Differential Problems |
| title_short | A Matrix Spline Method for a Class of Fourth-Order Ordinary Differential Problems |
| title_sort | matrix spline method for a class of fourth order ordinary differential problems |
| topic | matrix differential equations higher-order matrix splines numerical algorithms |
| url | https://www.mdpi.com/2227-7390/10/16/2826 |
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