Why Improving the Accuracy of Exponential Integrators Can Decrease Their Computational Cost?
In previous papers, a technique has been suggested to avoid order reduction when integrating initial boundary value problems with several kinds of exponential methods. The technique implies in principle to calculate additional terms at each step from those already necessary without avoiding order re...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-04-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/9/9/1008 |
| _version_ | 1797535791125102592 |
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| author | Begoña Cano Nuria Reguera |
| author_facet | Begoña Cano Nuria Reguera |
| author_sort | Begoña Cano |
| collection | DOAJ |
| description | In previous papers, a technique has been suggested to avoid order reduction when integrating initial boundary value problems with several kinds of exponential methods. The technique implies in principle to calculate additional terms at each step from those already necessary without avoiding order reduction. The aim of the present paper is to explain the surprising result that, many times, in spite of having to calculate more terms at each step, the computational cost of doing it through Krylov methods decreases instead of increases. This is very interesting since, in that way, the methods improve not only in terms of accuracy, but also in terms of computational cost. |
| first_indexed | 2024-03-10T11:50:17Z |
| format | Article |
| id | doaj.art-91fa4a89b70f4fd2bf53f1a5f8546c78 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T11:50:17Z |
| publishDate | 2021-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-91fa4a89b70f4fd2bf53f1a5f8546c782023-11-21T17:45:39ZengMDPI AGMathematics2227-73902021-04-0199100810.3390/math9091008Why Improving the Accuracy of Exponential Integrators Can Decrease Their Computational Cost?Begoña Cano0Nuria Reguera1Departamento de Matemática Aplicada, Facultad de Ciencias, Universidad de Valladolid, IMUVA, Paseo de Belén 7, 47011 Valladolid, SpainDepartamento de Matemáticas y Computación, Universidad de Burgos, IMUVA, Escuela Politécnica Superior, Avda. Cantabria, 09006 Burgos, SpainIn previous papers, a technique has been suggested to avoid order reduction when integrating initial boundary value problems with several kinds of exponential methods. The technique implies in principle to calculate additional terms at each step from those already necessary without avoiding order reduction. The aim of the present paper is to explain the surprising result that, many times, in spite of having to calculate more terms at each step, the computational cost of doing it through Krylov methods decreases instead of increases. This is very interesting since, in that way, the methods improve not only in terms of accuracy, but also in terms of computational cost.https://www.mdpi.com/2227-7390/9/9/1008avoiding order reductionefficiencyKrylov methods |
| spellingShingle | Begoña Cano Nuria Reguera Why Improving the Accuracy of Exponential Integrators Can Decrease Their Computational Cost? Mathematics avoiding order reduction efficiency Krylov methods |
| title | Why Improving the Accuracy of Exponential Integrators Can Decrease Their Computational Cost? |
| title_full | Why Improving the Accuracy of Exponential Integrators Can Decrease Their Computational Cost? |
| title_fullStr | Why Improving the Accuracy of Exponential Integrators Can Decrease Their Computational Cost? |
| title_full_unstemmed | Why Improving the Accuracy of Exponential Integrators Can Decrease Their Computational Cost? |
| title_short | Why Improving the Accuracy of Exponential Integrators Can Decrease Their Computational Cost? |
| title_sort | why improving the accuracy of exponential integrators can decrease their computational cost |
| topic | avoiding order reduction efficiency Krylov methods |
| url | https://www.mdpi.com/2227-7390/9/9/1008 |
| work_keys_str_mv | AT begonacano whyimprovingtheaccuracyofexponentialintegratorscandecreasetheircomputationalcost AT nuriareguera whyimprovingtheaccuracyofexponentialintegratorscandecreasetheircomputationalcost |