A Sparse Spectral Method for Volterra Integral Equations Using Orthogonal Polynomials on the Triangle
| Autor: | Timon S. Gutleb, Sheehan Olver |
|---|---|
| Přispěvatelé: | The Leverhulme Trust |
| Rok vydání: | 2020 |
| Předmět: |
Numerical Analysis
math.NA Volterra operator 65N35 45D05 0103 Numerical and Computational Mathematics Applied Mathematics Numerical & Computational Mathematics Numerical Analysis (math.NA) Bivariate analysis Volterra integral equation Domain (mathematical analysis) 0101 Pure Mathematics Computational Mathematics symbols.namesake Nonlinear Sciences::Exactly Solvable and Integrable Systems 0102 Applied Mathematics Orthogonal polynomials FOS: Mathematics symbols Quantitative Biology::Populations and Evolution Applied mathematics Mathematics - Numerical Analysis Spectral method Mathematics |
| Zdroj: | SIAM Journal on Numerical Analysis. 58:1993-2018 |
| ISSN: | 1095-7170 0036-1429 |
| DOI: | 10.1137/19m1267441 |
| Popis: | We introduce and analyse a sparse spectral method for the solution of Volterra integral equations using bivariate orthogonal polynomials on a triangle domain. The sparsity of the Volterra operator on a weighted Jacobi basis is used to achieve high efficiency and exponential convergence. The discussion is followed by a demonstration of the method on example Volterra integral equations of the first and second kind with known analytic solutions as well as an application-oriented numerical experiment. We prove convergence for both first and second kind problems, where the former builds on connections with Toeplitz operators. Comment: 24 pages, 4 figures |
| Databáze: | OpenAIRE |
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