A Second-Order Time Discretization for Second Kind Volterra Integral Equations with Non-Smooth Solutions
In this paper, a novel second-order method based on a change of variable and the symmetrical and repeated quadrature formula is presented for numerical solving second kind Volterra integral equations with non-smooth solutions. Applying the discrete Grönwall inequality with weak singularity, the conv...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2023-06-01
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| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/11/12/2594 |
| Summary: | In this paper, a novel second-order method based on a change of variable and the symmetrical and repeated quadrature formula is presented for numerical solving second kind Volterra integral equations with non-smooth solutions. Applying the discrete Grönwall inequality with weak singularity, the convergence order <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="script">O</mi><mo>(</mo><msup><mi>N</mi><mrow><mo>−</mo><mn>2</mn></mrow></msup><mo>)</mo></mrow></semantics></math></inline-formula> in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>L</mi><mo>∞</mo></msup></semantics></math></inline-formula> norm is proved, where <i>N</i> refers to the number of time steps. Numerical results are conducted to verify the efficiency and accuracy of the method. |
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| ISSN: | 2227-7390 |